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
[tex]\begin{cases}12x-9y = -69\\ -12x-8y = -16\end{cases}[/tex]
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.
