Question 7687
So we start with

4x + 3y = 59
2x + 3y = 43

What we're going to do is eliminate one of the variables. By the looks of it, you've got a 3y on both equations. That's very nice of them because it makes it easier.


We're actually going to use a trick here. We're going to multiply the second equation by -1. BTW, doing this does NOT alter the equation. It just changes its appearance. So now you've got:


4x + 3y = 59
-2x - 3y = -43


Now calculate downwards like you did. You should get

2x = 16 <------ The 3y's cancel to 0.
x = 8.


Now to get the y, you can plug in the x = 8 in any of the two equations. You WILL get the same y-value. Let's just pick the first one:


4(8) + 3y = 59 ---> 32 + 3y = 59 ---> 3y = 27 ---> y = 9.


Let's try to do the second one just to see:


2(8) + 3y = 43 ---> 16 + 3y = 43 ---> 3y = 27 ---> y = 9. AHA! Same answer!

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What happens, then, if all of the coefficients are different? What do you do? Stay tuned.