Question

Can somebody find the solution to this question

Answer 1

Answer:  (x,y) = (-2, 5)

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Explanation:

4x-3y = -23 is the same as 12x-9y = -69 when we multiply both sides by 3

-3x-2y = -4 is the same as -12x-8y = -16 when we multiply both sides by 4

Our updated system looks like this

$\begin{cases}12x-9y = -69\\ -12x-8y = -16\end{cases}$

Notice how we have 12x and -12x. They combine to 0x allowing the x terms to go away.

The y terms combine to -9y+(-8y) = -17y and the right hand sides combine to -69+(-16) = -85

After doing those three sets of additions, we get the new equation -17y = -101 which solves to y = -85/(-17) = 5

The last step is to use this y value to find x

4x-3y = -23

4x-3(5) = -23

4x-15 = -23

4x = -23+15

4x = -8

x = -8/4

x = -2

So the solution is (x,y) = (-2, 5)

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Check:

Let's plug the solution into the first equation

4x-3y = -23

4(-2)-3(5) = -23

-8-15 = -23

-23 = -23

We get a true result. Let's do the same for the second equation

-3x-2y = -4

-3(-2) - 2(5) = -4

6 - 10 = -4

-4 = -4

This result is true as well. So we've confirmed both equations to fully confirm the solution of this system.