UNIT: LINEAR SYSTEMS
In the system of equations below, which variable would it be easiest to solve for? The easiest to solve for is x in the first equation. The easiest to solve for is y in the first equation. The easiest to solve for is x in the second equation. The easiest to solve for is y in the second equation.
The easiest to solve for is x in the first equation.
Which equation results from adding the equations in this system?
-8y=6
The system of linear equations and is graphed below.How many solutions does the system of equations have? 0 1 3 4
0
Use the linear combination method to solve this system of equations. What is the value of x? 0 1 4.8
1
Which is true regarding the system of equations? The system results in a false statement. The system results in an intersection at one point. The system results in parallel lines. The system results in a true statement because they are the same line.
notThe system results in parallel lines.
Which values for A and B will create infinitely many solutions for this system of equations? , , , ,
not a=6, b=15
Which graph represents this system? 2x-5y=-5 y=2/5x+1
not b
What is the solution to the system of linear equations graphed below?
(-2 1/2 , -2)
What is the solution to the system of equations? (2, -5) (-2, 5) (-2, -5) (2, 5)
(-2, 5)
Which ordered pair is a solution to the system of linear equations and ? (-4, -3) (-4, 3) (-3, -4) (-3, 4)
(-3, -4)
Which ordered pair is the solution to the system of linear equations and ?
NOT (-1,5)
Manuel and Sonja are shopping for school supplies. Manuel is buying 5 notebooks and 3 pens at a cost of $21. Sonja is buying 6 notebooks and 5 pens at a cost of $28. The first equation, representing Manuel's purchase, is . What is the second equation needed to solve the system?
d
Consider the graph with four lines below. By inspection, which system would have no solution? line a and line b line a and line c line b and line c line b and line d
line b and line c
The equations in the system below are parallel. How many solutions does the system have? no solution one unique solution two solutions an infinite number of solutions
no solution
Sonji went to a sandwich shop for lunch with 8 of her friends. Part of the group ordered only a sandwich for $5, and the rest of the group ordered a combo for $8. The bill for all 9 people totaled $66.00. Which system of equations represents the number of meals of each type that Sonji and her friends purchased?
not d
Which graph represents this system? 3x+2y+-6 y=- 3/2x+2
not d
What is the value of y in this system of equations?
-21
Multiply each equation by a constant that would help to eliminate the y terms.What are the resulting equations?
not c
The equations in this sytem were added to solve for x. What is the value of x?
x=2
What is the solution to the system of equations? (1, -5) (1, 5) (-1, -5) (-1, 5)
(1, -5)
What is the solution to this system of equations? no solution infinitely many solutions
(4, - 1/4)
What is the solution to this system of equations? no solution infinitely many solutions
(4,2)
What is the value of x in this system of equations? Express the answer as a decimal rounded to the nearest tenth.
11.2
Which system of equations has only one solution?
2x+4y=6 3x-4y=9
Which system of equations has no solution?
3x-6y=4 and -4x+8y=7
Which equation results from adding the equations in this system?
3x=3
Which equation results from adding the equations in this system?
7x=-35
Which equation results from adding the equations in this system?
8y=-6
Bryce took a quiz that consisted of true-or-false questions and multiple-choice questions. The true-or-false questions were worth 1 point each, and the multiple-choice questions were worth 2 points each. Bryce only knows that he answered 8 questions correctly and earned a total of 14 points. To determine the number of each type of question that he answered correctly, he wrote the system of linear equations and . Which ordered pair is a solution to this system of linear equations, and what does the ordered pair represent? ; Bryce answered 0 true-or-false questions correctly and 8 multiple-choice questions correctly. ; Bryce answered 2 true-or-false questions correctly and 6 multiple-choice questions correctly. ; Bryce answered 6 true-or-false questions correctly and 2 multiple-choice questions correctly. ; Bryce answered 8 true-or-false questions correctly and 0 multiple-choice questions correctly.
; Bryce answered 2 true-or-false questions correctly and 6 multiple-choice questions correctly.
Dimitri determined that the ordered pair (2, -2) is a solution to the system of linear equations 7x + 9y = -4 and 5x - 2y= 6 as shown.What was Dimitri's mistake? He mixed up the coordinates of the ordered pair when substituting it into the equations 7x + 9y = -4 and 5x - 2y = 6. He checked the equation 7x + 9y = -4 first when he should have checked first. He made a mistake in his calculations when substituting the ordered pair into the equation 7x + 9y = -4 and simplifying. He made a mistake in his calculations when substituting the ordered pair into the equation 5x - 2y = 6 and simplifying.
He made a mistake in his calculations when substituting the ordered pair into the equation 5x - 2y = 6 and simplifying.
Jon has to choose which variable to solve for in order to be able to do the problem below in the most efficient manner. Which variable should he choose so that he can use substitution to solve the system? Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y. Jon should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x. Jon should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y. Jon should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Claire completed the steps to solve the system of equations. Step 1Step 2Step 3 Step 4Step 5Solution is .Is Claire's solution to the system of equations correct? Explain why or why not. No, Claire should have multiplied the second equation by negative two instead of positive two in step one. Yes, Claire correctly added the equations and then substituted for x to solve for y. No, Claire should have multiplied the first equation by negative three instead of positive three in step one. No, Claire should have gotten instead of in step four.
No, Claire should have gotten instead of in step four.
Which constants could each equation be multiplied by to eliminate the x-variable using addition in this system of equations? The first equation can be multiplied by -3 and the second equation by 2. The first equation can be multiplied by -4 and the second equation by 2. The first equation can be multiplied by 3 and the second equation by 2. The first equation can be multiplied by 4 and the second equation by -3.
The first equation can be multiplied by 3 and the second equation by 2.
The scouts sold small and large boxes of cookies as a fund raiser. One scout sold 7 small boxes and 12 large boxes for $54.00. Another scout sold 5 small boxes and 10 large boxes for $60.00. The scout leader wrote a system of equations to represent the their sales.Which constants can each equation be multiplied by so that one variable is eliminated when the equations are added? Check all that apply. The first equation can be multiplied by 5 and the second equation by -6 to eliminate the y. The first equation can be multiplied by -5 and the second equation by 6 to eliminate the y. The first equation can be multiplied by -5 and the second equation by 7 to eliminate the x. The first equation can be multiplied by 5 and the second equation by -7 to eliminate the x. The first equation can be multiplied by -5 and the second equation by 10 to eliminate the x.
The first equation can be multiplied by 5 and the second equation by -6 to eliminate the y. The first equation can be multiplied by -5 and the second equation by 6 to eliminate the y. The first equation can be multiplied by -5 and the second equation by 7 to eliminate the x. The first equation can be multiplied by 5 and the second equation by -7 to eliminate the x.
Sophia's math test is worth 130 points and has 40 problems. Each problem is worth either 4 points or 3 points. How many of each question type were on the test? The test had 30 4-point questions and 10 3-point questions. The test had 10 4-point questions and 30 3-point questions. The test had 28 4-point questions and 12 3-point questions. The test had 25 4-point questions and 10 3-point questions.
The test had 10 4-point questions and 30 3-point questions.
Dan and Mario went to a sandwich shop to buy sandwiches for their group of friends. Dan bought 2 tuna and 5 vegetarian sandwiches for $37. Mario bought 4 tuna and 3 vegetarian sandwiches for $39. Which system of equations can be used to solve for the cost of each kind of sandwich?
a
Which statements about this system of equations are true? Check all that apply The x-variable will be eliminated when adding the system of equations. The y-variable will be eliminated when adding the system of equations. The sum of the system of equations is . There are infinitely many solutions to the system of equations.
The x-variable will be eliminated when adding the system of equations. The sum of the system of equations is . y=-3
Johann and Marta shopped at a vintage toy store. Johann bought 3 blue marbles and 5 green marbles and paid $11. Marta bought 4 blue marbles and 2 green marbles and paid $10. Which system of equations can be used to find the prices of the blue and green marbles?
b
Consider the system of equations and the partial solution below. Multiply the first equation by -4.Multiply the second equation by 3.Add the resulting system of equations.Which terms will cancel when you add the resulting system of equations? and 36 and and and
d
Fiona and Iliana went to a going-out-of-business sale at a local video store. The store was advertizing all HD videos on sale for one price and all classic videos for a different price. Fiona bought 5 HD videos and 2 classic videos for $31. Iliana bought 5 classic videos and 3 HD videos for $30. Which system of equations can be used to find the prices of the classic and HD videos?
d
Kendra was given this system of equations. Kendra's work is shown in the table. Where, if anywhere, did Kendra first make a mistake? StepsKendra's WorkStep 1Step 2Step 3 step 1 step 2 step 3 no mistake
no mistake
What is the solution to this system of equations? (1, ) (0, 8) infinitely many solutions no solution
no solution
A system of equations is shown on the graph below.How many solutions does this system have? no solutions one unique solution two solutions an infinite number of solutions
no solutions
Which system of equations has infinitely many solutions?
not -x+2y=6 7x-2y=12
Which statements about this system of equations are true? Check all that apply. The x-variable will be eliminated when adding the system of equations. The y-variable will be eliminated when adding the system of equations. The sum of the system of equations is . There is only one solution to the system of equations.
not The y-variable will be eliminated when adding the system of equations. There is only one solution to the system of equations. x=2
Which statements about this system of equations are true? Check all that apply. The x-variable will be eliminated when adding the system of equations. The y-variable will be eliminated when adding the system of equations. The sum of the system of equations is . There is only one solution to the system of equations.
not The y-variable will be eliminated when adding the system of equations. x=2
Use the linear combination method to solve this system of equations. What is the value of x? 0 1 4.8
not -1
Petro was given this system of equations. Petro's work is shown in the table. Where, if anywhere, did Petro first make a mistake? StepsPetro's WorkStep 1Step 2Step 3 step 1 step 2 step 3 no mistake
step 3
The equations in this sytem were added to solve for x. What is the value of x?
x=1
The solution to a system of linear equations is . Which system of linear equations has this point as its solution? and and and and
x-5y=12 and 3x+2y=-15
The graphed line shown below is . Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
y+1=3x
The graphed line shown below is . Which equation, when graphed with the given equation, will form a system that has infinitely many solutions?
y=-(2x+8)
Arnoldo needs to write this system in slope-intercept form. Which shows how he could do that?
y=3/2x-3
Consider this system of equations. Which equation represents the first equation written in slope-intercept form?
y=5/2x-5
Consider the following system of equations given in slope-intercept form. y = −13x + 17, y = 5x - 23 Use the graphing calculator to determine the best window range to find the point of intersection. -10 x 10, -10 y 10 -20 x 0, -20 y 0 0 x 20, 0 y 20 20 x 40, 20 y 40
0 x 20, 0 y 20
Which ordered pair is the solution to the system of linear equations and ?
NOT (3, -1)
Which graph represents this system? y=1/2x+3 y=3/2x-1
a
A radio plays 16 commercials in an hour. A commercial is either 30-seconds long or 60-seconds long. The total commercial time is 13 minutes. If x represents a 30-second commercial and y is a 60-second commercial, which equations would you enter into a graphing calculator to find how many of each type of commercial is played? Check all that apply. x + y = 13 x + y = 16 0.5x + y = 13 0.5x + y = 16 0.5x + y = 29
x + y = 16 0.5x + y = 13
Mr. Berger assigned the following system of equations to be solved for homework. Which is the x-coordinate of the correct solution?
x=-3
Theo solved the following problem correctly for homework. What is the y-coordinate of his solution?
y=5
The graphed line shown below is . Which equation, when graphed with the given equation, will form a system that has no solution?
y=5(x+2)
The system of linear equations and is graphed below.What is the solution to the system of equations? (-3, 2) (-2, 3) (2, -3) (3, 2)
(-3, 2)
Betty correctly determined that the ordered pair (-3, 5) is a solution to the system of linear equations and x+ 4y = 17. Based on this information, which statement is correct? (-3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17. (-3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17. (-3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7. (-3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.
(-3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.
What is the solution to this system of equations? What is the solution to the system of equations? (-6, -2) (-2, 6) (6, 2) (-2, -6)
(-6, -2)
Which ordered pair is the solution to the system of linear equations and ? (-4, 6) (6, -4) (-4, -6) (-6, -4)
(-6, -4)
What is the solution to the system of equations graphed below?
(2,-3)
What is the solution to the system of equations?
(2,-3)
What is the solution to the system of linear equations graphed below?
(3 1/2, -4)
The system of linear equations and is graphed below.What is the solution to the system of equations? (-4, 3) (-3, 4) (3, -4) (4, -3)
(3, -4)
The first line in the system of equations is graphed on the coordinate plane. Graph the second line to find the solution to the system.Kaden's GraphWhat is the solution to the system of equations? no solution infinitely many solutions (4, -3) (1.5, -1.75)
(4, -3)
Herky was given the following system of equations to solve.What is the solution to the system?
(7,2)
Consider the system of equations given in slope-intercept form. y = −13x + 17, y = 5x - 23 The solution seems to be about (8, 14). Use the graphing calculator to find the exact values for the intersection point. What is the solution to this system of equations? (, )
(7.5, 14.5)
Jerome bought 15 videos from a department store. Some videos were new releases, x, which cost $19, and some videos were classics, y, which cost $8. He spent a total of $164 on the videos. Which system of equations is set up correctly to model this information?
a
Sonji went to a sandwich shop for lunch with 8 of her friends. Part of the group ordered only a sandwich for $5, and the rest of the group ordered a combo for $8. The bill for all 9 people totaled $66.00. Which system of equations represents the number of meals of each type that Sonji and her friends purchased?
a
Which graph represents this system? y=3 x+y=4
a
Which graph represents this system? y=1/2x+3 y=3/2x+-3
a
Which is true regarding the system of equations? The system results in a false statement. The system results in an intersection at one point. The system results in parallel lines. The system results in a true statement because they are the same line.
a
Which shows the correct first step to solving the system of equations in the most efficient manner?
a
The equations in the system below are equivalent. How many solutions does the system have? no solution one unique solution two solutions an infinite number of solutions
an infinite number of solutions
Murray's father deposited $6,000 of his savings into two accounts. One account earns 1.5 percent interest, and the other account earns 2.5 percent interest. At the end the year, the interest in the account that earned 2.5 percent was $110.00 more than the other account. Which system represents the amounts of money, x and y, that was put into each account?
b
Murray's father deposited $6,000 of his savings into two accounts. One account earns 1.5 percent interest, and the other account earns 2.5 percent interest. At the end the year, the interest in the account that earned 2.5 percent was $110.00 more than the other account. Which system represents the amounts of money, x and y, that was put into each account?
c
Which equations are equivalent to when written in slope-intercept form? Check all that apply.
2x-3y=12 -4(2x-3y)=-4(12)
A system of equations is shown on the graph below.How many solutions does this system have? no solutions one unique solution two solutions an infinite number of solutions
one unique solution
Consider the equation . Which equation, when graphed with the given equation, will form a system with infinitely many solutions?
y+2x=3
The graphed line shown below is . Which equation, when graphed with the given equation, will form a system that has no solution?
NOT y=5(x-2)
Binh solved this system of equations by graphing.Binh's GraphWhich statements identify the errors Binh made? Check all that apply. Binh incorrectly graphed the equation . Binh should have graphed the y-intercept of at . Binh should have graphed the y-intercept of at . Binh incorrectly graphed the equation . Binh should have found the point of intersection to be .
(a)Binh incorrectly graphed the equation . (b)Binh should have graphed the y-intercept of at . (E)Binh should have found the point of intersection to be .
Jessie graphed one of the lines in a system of equations: . If the system has an infinite number of solutions, which statements are true? Check all that apply. Any point in the coordinate plane is a solution because it has an infinite number of solutions. Point (1, 1) is a solution because it is one of the points on the line already graphed. It is impossible to tell if (-1,-5) is a solution without seeing the other line graphed. Point (20, 58) is a solution because it results in a true statement when the point values are substituted into the equation of the line. When the other line in the system is graphed, it will share all points with the line already graphed.
(b)Point (1, 1) is a solution because it is one of the points on the line already graphed. (D) Point (20, 58) is a solution because it results in a true statement when the point values are substituted into the equation of the line. (E)When the other line in the system is graphed, it will share all points with the line already graphed.
Which system of linear equations has the ordered pair (4, -5) as a solution? and and and and
3x-2y=22 and 2x+9y=-37
Every hour, the radio station plays 16 commercials that are a total 13 minutes in length. If x represents a 30-second commercial and y is a 60-second commercial, how many of each type of commercial is played? Enter the equations that represent the scenario into the graphing calculator to find how many of each type of commercial is played. x + y = 16 0.5x + y = 13 In one hour, the radio station plays 4✔ 681012 commercials that are 30 seconds long. In one hour, the radio station plays 468✔ 1012 commercials that are 60 seconds long.
6 and 10
Coretta wants to create a system of equations so that the system has only one solution. Which of these can Coretta do? Check all that apply. Create a pair of equivalent equations. Create a pair of lines in which one line lies directly on top of the other. Create a pair of equations with different slopes. Create a pair of lines that will always stay the same distance apart. Create a pair of lines that intersect at only one point.
Create a pair of equations with different slopes. Create a pair of lines that intersect at only one point.
Antoinette needs to solve this system of equations by graphing. Which statements explain how she should graph the equations? Check all that apply. She should rewrite both equations in slope-intercept form. She should rewrite the first equation in slope-intercept form. She should find that the second equation has a slope of 4. When rewriting the first equation, she should subtract 2x from each side of the equation to get -7y by itself. After rewriting the first equation in slope-intercept form, she should find that both lines have negative slopes.
NOT She should find that the second equation has a slope of 4. She should rewrite both equations in slope-intercept form.
The graph below represents a system of equations. By observation, what is the solution to this system? (0, -3) (-3, 0) no solution infinitely many solutions
NOT (-3,0)
Which ordered pair is the solution to the system of linear equations and ? (-4, 6) (6, -4) (-4, -6) (-6, -4)
NOT (-4, -6)
Which ordered pair is the solution to the system of linear equations and ?
NOT (1,-3)
Which ordered pair is the solution to the system of linear equations and ?
NOT (5,-1)
Emma was given a system of equations to solve by graphing. Which statement correctly identifies Emma's error?Emma's Graph Line 1 should have a y-intercept at (0, 2). Line 2 should have a y-intercept at (0, 2). Line 1 should have a slope of 2. Line 2 should have a slope of -5.
NOT Line 1 should have a slope of 2.
Juliet needs to rewrite in slope-intercept form so she can easily graph it. Which step would be correct to start the process? She could combine the x and 2 to get . She could divide both sides by 3 to get . She could distribute the 3 to get . She could subtract the 6y to get .
NOT She could distribute the 3 to get .
If the four lines are extended, which system would have only one solution? line a and line b line b and line c line b and line d line c and line d
NOT line b and line d
The graph for the equation is shown below. If another equation is graphed so that the system has no solution, which equation could that be?
NOT y=- 1/2x+2
Beth wrote a system of equations to determine when a referee will earn the same salary working the East Conference and West Conference games. y = 40x − 25 and y = 35x − 5 (x = total games and y = amount earned) Beth determined that at 135 games, the referee would earn the same salary for each conference game. Is she correct? Yes, Beth is correct. No. She did not find the correct intersection point. No. She only estimated and did not find the exact values. No. She interpreted the solution of (4, 135) incorrectly.
No. She interpreted the solution of (4, 135) incorrectly.
Antoinette needs to solve this system of equations by graphing. Which statements explain how she should graph the equations? Check all that apply. She should rewrite both equations in slope-intercept form. She should rewrite the first equation in slope-intercept form. She should find that the second equation has a slope of 4. When rewriting the first equation, she should subtract 2x from each side of the equation to get -7y by itself. After rewriting the first equation in slope-intercept form, she should find that both lines have negative slopes.
She should rewrite the first equation in slope-intercept form. When rewriting the first equation, she should subtract 2x from each side of the equation to get -7y by itself.
Miguel used the graph below to represent a system of equations. Which statement is the best conclusion for Miguel's system? Since the lines do not intersect, this system has no solution. Since the lines will intersect at one point, this system has one solution. Since the lines will intersect at two points, this system has two solutions. Since the lines will intersect at many points, the system has many solutions.
Since the lines will intersect at one point, this system has one solution.
In this system of equations, which variable would it be easiest to solve for? The easiest to solve for is x in the first equation. The easiest to solve for is y in the first equation. The easiest to solve for is x in the second equation. The easiest to solve for is y in the second equation.
The easiest to solve for is x in the first equation.
Consider the system of equations shown below. When graphed, the system consists of two lines that will never meet, no matter how far they are extended. Why are the lines parallel? The linear equations have the same slope and y-intercept. The linear equations have different slopes and y-intercepts. The linear equations have the same slope but different y-intercepts. The linear equations have different slopes but the same y-intercept.
The linear equations have the same slope but different y-intercepts.
Consider the system of linear equations 2x + 3y = 8 and 3x + y = -2. Which statement is correct? The point (1, 2) is not a solution to the system of equations because it satisfies neither equation. The point (1, 2) is not a solution to the system of equations because it does not satisfy the equation 3x + y = -2. The point (1, 2) is a solution to the system of equations because it satisfies the equation 2x + 3y = 8. The point (1, 2) is a solution to the system of equations because it satisfies both equations.
The point (1, 2) is not a solution to the system of equations because it does not satisfy the equation 3x + y = -2.
Which statement is correct about the system of linear equations graphed below? The system of equations has one solution because the lines will eventually intersect. The system of equations has one solution because the lines will never intersect. The system of equations does not have one solution because the lines will eventually intersect. The system of equations does not have one solution because the lines will never intersect.
The system of equations does not have one solution because the lines will never intersect.
Suppose that when a system of linear equations is graphed, one line completely overlaps the other line. Which statement is correct? The system of equations has one solution because the lines intersect at one point. The system of equations has one solution because the lines do not intersect at only one point. The system of equations does not have only one solution because the lines intersect at one point. The system of equations does not have only one solution because the lines do not intersect at only one point.
The system of equations does not have only one solution because the lines do not intersect at only one point.
Which is true regarding the system of equations? The system results in a false statement. The system results in an intersection at one point. The system results in many solutions because they are the same line. The system results in a true statement.
The system results in a false statement.
Which is true regarding the system of equations? The system results in a false statement. The system results in an intersection at one point. The system results in parallel lines. The system results in a true statement because they are the same line.
The system results in a true statement because they are the same line.
Jerry solved the system of equations.As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement? The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution. The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7. The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2. The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.
The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Malik solved this system of equations.As the first step, he decided to solve for x in the first equation because it has a small, even number for the coefficient. Jill told him there was a more efficient way. What reason can Jill give for her statement? The variable y in the second equation has a coefficient of one so there will be fewer steps to the solution. The variable x in the second equation has a coefficient of 5 so it will be easy to divide 15 by 5. The variable y in the first equation is divisible by 2 so it will be the most efficient way to start. The variable y in the first equation has a larger even number. When dividing by 4, the solution will be a smaller number.
The variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.
The Panthers, a high school basketball team, charges $6 for adult tickets and $3 for children's tickets. If 120 people went to the most recent game, and the total earnings for ticket sales was $612, how many children went to the game? There were 36 children at the game. There were 50 children at the game. There were 84 children at the game. There were 108 children at the game.
There were 36 children at the game.
Trang graphed the system of equations below.Trang says that the system of equations has no solution. Which explains whether or not he is correct? Trang is correct because the lines have the same slope but different y-intercepts. Trang is correct because the lines have the same slope and the same y-intercept. Trang is not correct because the lines have the same slope but different y-intercepts. Trang is not correct because the lines have the same slope and the same y-intercept.
Trang is correct because the lines have the same slope but different y-intercepts.
Malik solved this system of equations.As the first step, he decided to solve for x in the first equation because it has a small, even number for the coefficient. Jill told him there was a more efficient way. What reason can Jill give for her statement? The variable y in the second equation has a coefficient of one so there will be fewer steps to the solution. The variable x in the second equation has a coefficient of 5 so it will be easy to divide 15 by 5. The variable y in the first equation is divisible by 2 so it will be the most efficient way to start. The variable y in the first equation has a larger even number. When dividing by 4, the solution will be a smaller number.
he variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.
What is the solution to the system of equations below?
not (-7,24)
What is the solution to the system of equations below?
not (24,-7)
Jon has to choose which variable to solve for in order to be able to do the problem below in the most efficient manner. Which variable should he choose so that he can use substitution to solve the system? Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y. Jon should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x. Jon should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y. Jon should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
not Jon should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
In the system of equations, which variable would it be easiest to solve for? The easiest to solve for is x in the first equation. The easiest to solve for is y in the first equation. The easiest to solve for is x in the second equation. The easiest to solve for is y in the second equation.
not The easiest to solve for is y in the first equation.
The measures of two supplementary angles total 180 degrees. The measure of angle y is 65 degrees less than the measure of angle x. What are the measures of the angles? The measure of angle x is 122.5 degrees. The measure of angle y is 57.5 degrees. The measure of angle x is 115 degrees. The measure of angle y is 65 degrees. The measure of angle x is 57.5 degrees. The measure of angle y is 122.5 degrees. The measure of angle x is 65 degrees. The measure of angle y is 115 degrees.
not The measure of angle x is 115 degrees. The measure of angle y is 65 degrees.
Which graph represents this system? y=2x+1 y=-4x+7
not b
Which graph represents this system? 2x-5y=-5 y=2/5x+1
not c
Which graph represents this system? y=2x+1 y=-4x+7
not c
The graph for the equation is shown below. If another equation is graphed so that the system has an infinite number of solutions, which equation could that be?
y=- 1/4(4x-8)
Which equation is written in slope-intercept form?
y=3x-2
Consider this system of equations. Which shows the second equation written in slope-intercept form?
y=5x+3
Consider this system of equations. Which shows the first equation written in slope-intercept form?
y=7x-5
Consider the system of equations in standard form. x + 4y = 26, 3x - 4y = 30 What is the best window range for the x-values to determine the solution?x-min = 0, x-max = 5x-min = 5, x-max = 10✔ x-min = 10, x-max = 15x-min = 15, x-max = 20 What is the best window range for the y-values to determine the solution?✔ y-min = 0, y-max = 5y-min = 5, y-max = 10y-min = 10, y-max = 15y-min = 15, y-max = 20 What is the exact solution to the system of equations?(10, 0)(10, 4)✔ (14, 3)(15, 2.75)
✔ x-min = 10, x-max = 15 ✔ y-min = 0, y-max = 5 (14,3)