Question

A system of equations is shown below:

2x = 5y + 4
3x − 2y = −16

What is the solution to this system of equations? (5 points)

Answer 1

So the answer is
X = -8
Y = -4
Here is the working

Answer 2

x = -8, y = -4

Explanation:

First we want to write the equations so the variables line up

`2x - 5y = 4\\3x - 2y = -16\\`

Next, we could either multiply one of the equations to cancel out the x's or the y's, either one works.

I will choose to cancel out the x's

`-3R_1 + 2R_2\\-6x + 15y = -12\\6x - 4y = -32`

add the equations and solve

`11y = -44\\y = -4`

once you have one variable, you can use it to solve the other

`2x - 5(-4) = 4\\2x + 20 = 4\\2x = -16\\x = -8`

verify

`3(-8) - 2(-4)\\-24+ 8\\-16\\`

it works