Question

What is the answer a, b, c, or d

Answer 1

Answer: Choice B

(-2, 5)

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Step-by-step explanation:

The original system is

`\begin{cases}-4x+3y = 23\\ x-y = -7\end{cases}`

Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations

`\begin{cases}-4x+3y = 23\\ 3x-3y = -21\end{cases}`

Now add straight down

The x terms add to -4x+3x = -1x = -x

The y terms add to 3y+(-3y) = 0y = 0

The terms on the right hand sides add to 23+(-21) = 2

We end up with the equation -x = 2 which solves to x = -2

Now use this to find y. You can pick any equation with x,y in it

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-4x+3y = 23

-4(-2)+3y = 23

8+3y = 23

3y = 23-8

3y = 15

y = 15/3

y = 5

Or

x-y = -7

-2-y = -7

-y = -7+2

y = -5

y = 5

Either way, we get the same y value.

So that's why the solution is (x,y) = (-2, 5)