Question

Question 8 (Essay Worth 2 points)

(05.03 MC)

A system of equations is given.

3y = 20 - 4x
2y = 12 - 3x

Solve for (x, y) using the elimination method. Show all work.

Answer 1

(-4,12)

Explanation:

rewrite the equations

3y = 20 - 4x → 3y + 4x = 20 → multiply by (-2) → -6y - 8x = -40

2y = 12 - 3x → 2y + 3x = 12 → multiply by (3) →6y + 9x = 36

x = -4

Substitute -4 for x into either of the original equations to solve for y.

3y = 20 - 4x

3y = 20 -4(-4)

3y = 20 + 16

3y = 36 Divide both sides by 3

y = 12

Helping in the name of Jesus.

Answer 2

(-1,8)

Explanation:

Hello! I'd be happy to help you solve this system of equations using the elimination method.

To use the elimination method, we want to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate y by multiplying the second equation by 3 and the first equation by 2 to get:

6y = 36 - 9x

-6y = -40 + 8x

Adding these two equations, we eliminate y and get:

0 = -4x - 4

Simplifying this equation, we get:

4x = -4

Dividing both sides by 4, we get:

x = -1

Now that we have found the value of x, we can substitute it into one of the original equations to find the value of y. Let's use the first equation:

3y = 20 - 4(-1)

3y = 24

Dividing both sides by 3, we get:

y = 8

Therefore, the solution to this system of equations is (x, y) = (-1, 8).