Question

A system of equations is shown below:

2x = 5y + 4
3x − 2y = −16

What is the solution to this system of equations?

(−8, −4)
(8, 4)
(−4, −8)
(4, 8)

Answer 1

(-8, -4)

Explanation:

Answer 2

(-8, -4) is the solution

Explanation:

Determine whether or not (-8, -4) is a solution to this system. It is a solution if we can substitute -8 for x and -4 for y in both equations and find that both equations are true:

2(-8) = 5(-4) + 4 TRUE

3(-8) - 2(-4) = -16 TRUE

So (-8, -4) is a solution to the given system.

Check out the second possible solution in the same way:

2(8) = 5(4) + 4 FALSE

Check out the third possible sol'n in the same way:

2(-4) = 5(4) + 4 FALSE

Check out the fourth in the same way:

2(4) = 5(8) + 4 FALSE

So we conclude that (-8, -4) is the sole solution to the given system.