Question

what is the solution of the system? Use elimination
5x+8y=-29
7x-2y=-67

Answer 1

Look at the 8y in the first equation and at the -2y in the second equation. If you add the equations the way they are now, nothing will eliminate, but if you multiply the entire second equation by 4, the y term will become -8y, and when added to the 8y of the first equation will be eliminated.

Answer 2

wait im confused where did 4 come from?

Answer 3

You need to do something so that when you add the 2 equations together one of the variables will add up to zero.

Answer 4

5x+8y=-29 (Equation A)
7x-2y=-67 (Equation B)
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We will be eliminating y first to solve x and then going back to plug in find y.
5x+8y=-29 (Equation A) - leaving it at +8y
7x-2y=-67 (Equation B) 0 multiply all by 4 so we can get -8y
7x*4-2y*4=-67*4 >>> 28x-8y=-268
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We will now subtract downward like you see in the equations below.
(A) 5x+8y=-29
(B) 28x-8y=-268
>33x+0y=-297
>33x=-297
>x=-297/33=-9
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Pick either one of the equation (A) or (B)
I will pick (A) where 5x+8y=-29 and now we know x=-9
5(-9)+8y=-29
-45+8y=-29
8y=-29+45
8y=16
y=16/8=2
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x=-9
y=2

Answer 5

Since in the frist equation there is 8y, and in the second equation there is -8y, if you multiply the second equation by 4, the -2y becomes -8y which when added to the 8y of the first equation will eliminate the y variable.