College Algebra (MA124) - 5.1 Homework

Determine whether the given ordered pair is a solution of the system. (1, -1) 6x+2y=4 7x-3y=3 Is (1, -1) a solution of the system?

not a solution

A solution to a system of linear equations in two variables is an ordered pair that:

satisfies both equations in the system

A​ company's _______ function is the money generated by selling x units of its product. The difference between this function and the​ company's cost function is called its​ ________ function.

- revenue - profit

When solving {2x+3y=13} {5x+2y=16} by the addition​ method, we can eliminate x by multiplying the first equation by 5 and the second equation by​ ________, and then adding the equations.

-2

When solving {x+6y=25} {3x+2y=-5} by the addition​ method, we can eliminate x by multiplying the first equation by​ ________ and then adding the equations.

-3

When solving {2x-2y=7} {y= 4x-5} by the substitution method, x=1/2 is obtained. Find the solution set.

The solution set is: {(1/2, -3)}

A company has a graph that shows the money it generates by selling x units of its product. It also has a graph that shows its cost of producing x units of its product. The point of intersection of these graphs is called the​ company's:

break-even point

Consider the following system: {20x-12y=16} {5x-3y=3} When solving this system by the addition method, 0=4 is obtained. What is the solution set?

the solution is the empty set - the equations in this system are called inconsistent - if the system is solved by graphing, two lines that are parallel will be obtained

Solve the system by the addition method. x+4y=-3 2x+5y=-3

the solution set is {(1,-1)}

Solve the system by the substitution method. x-2y=-3 y=-4x+6

the solution set is {(1,2)}

Solve the system of equations by the substitution method. x=3y-1 x=7y-5

the solution set is {(2,1)}

Solve the system by the addition method. 4x+8y=12 3x-8y=9

the solution set is {(3,0)}

Solve the system the addition method. x+y=8 x-y=-2

the solution set is {(3,5)}

Solve the system by the substitution method. x+y=-8 y=-3x

the solution set is: {(4, -12)}

Consider the following system: {x=4y+2} {3x-12y=6} When solving this system by the substitution​ method, 6equals6 is obtained. What is the solution​ set?

there are infinitely many solutions. the solution set is {(x,y)Ix=4y+2} or {(x,y)I 3x-12y=6} - the equations in this system are called dependent - if the system is solved by graphing, two lines that are identical (or coincide) will be obtained

Explain how to solve a system of equations using graphing.

to solve a system of linear equations byTo ​ graphing, graph both equations in the same rectangular coordinate system. For a system with one​ solution, the coordinates of the point of intersection of the lines is the​ system's solution.

Determine whether the given ordered pair is a solution of the system. (3, -3) y=3x-12 4x+6y=-6 Is (3, -3) a solution of the system?

yes

Let x represent one number and let y represent the other number. The sum of two numbers is -3. If one number is subtracted from the​ other, their difference is 13. Use the given conditions to write a system of equations. Solve the system and find the numbers.

{x+y=-3} {x-y=13}