Algebra I - Unit 4: Systems of Equations and Inequalities

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810. What is the administration fee?

$60

Which is the approximate solution to the system y = 0.5x + 3.5 and y = −2/3x + 1/3 shown on the graph?

(-2.7, 2.1)

What is the solution to this system of linear equations? 7x - 2y = -6 8x + y = 3

(0, 3)

The solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution?

(2, 0)

What is the solution to this system of linear equations? x + y = 4 x − y = 6

(5, −1)

Two linear equations are shown. ID: Graph with two linear equations, one is red noted as 'y = 1/3x + 2', the other is blue noted as 'y = 4/3x - 5' What is the solution to the system of equations?

(7, 13/3)

Gillian purchased 25 books at the library book sale. Each hardcover book cost $1.50, and each paperback book cost $0.50. Gillian spent a total of $26.50. The book costs can be represented by the system of equations below. h + p = 25 1.50h + 0.50p = 26.50 How many paperback books did Gillian buy?

11

A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Which inequality represents the possible ways Nina can eat 12 or more grams of protein, if x is the number of cheese squares that she eats and y is the number of turkey slices that she eats?

12 ≤ 2x + 3y

Which value of m will create a system of parallel lines with no solution? y=mx-6 8x-4y=12

2

Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking. Which combination of loaves of bread and batches of muffins could Helena bake?

2 loaves of bread and 4 batches of muffins

A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo. A private contractor charges $75 per hour to develop a logo plus a $100 supply fee. Which equation can be solved to determine x, the number of hours after which the costs would be the same?

50x + 250 = 75x + 100

Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, l. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, l. w ≥ 0.5l 2l + 2w ≤ 180 What is the maximum length possible for her blanket?

60 inches

What is the value of y in the solution to the system of equations? 1/3x + 1/4y = 1 2x - 3y = -30

8

A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x, and a certain number of pillows that come in pairs, y. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

Graph D; or the graph where the line passed both y = 2 and x = 4 with the shaded portion above the line

A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

Graph D; or the linear equation that passed both y= 4 and x= 2, and is shaded on the right-side of the line

To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 4x − 3y = 34 Second equation: 3x + 2y = 17

The first equation should be multiplied by 2 and the second equation by 3.

Which description of the graph of the linear inequality y ≥ 7x - 4 is correct?

The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test?

The test contains 10 three-point questions and 14 five-point questions.

Which ordered pairs make both inequalities true? y < 5x + 2 y > 1/2x + 1

[C] (1, 2) [E] (2, 2)

The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b?

a + b ≥ 30 b ≥ a + 10

Anatoliy has a combination of 104 nickels and quarters totaling $22. Which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, Anatoliy has?

n + q = 104 0.05n + 0.25q = 22

y = 5x - 1 -15x - 3y = 3 How many solutions does this linear system have?

one solution: (0, -1)

At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?

x + y > 12

The graph of a system of inequalities is shown. Graph ID: two overlapping linear equations, one is represented with blue and is a dotted line, the other is represented with red and is a solid line. Which system is represented by the graph?

y > 2x x + 2y ≤ -8

Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph?

y>−2x+2