How do you find x and y? I keep doing guess and check and it takes a long time. please tell me any shortcuts, if you have any. Thanks!

3x+2y=7
2x+3y=8

1 Answer
Feb 6, 2018

You can use elimination or substitution to solve this. I will show you elimination because I prefer it. Someone else can do substitution. (Besides, this message is long enough already >_<).

Elimination:
We want to make either x or y have the same coefficient. Let's use x:
3x + 2y=7
2x+3y=8


2(3x+2y)=2(7)
3(2x+3y)=3(8)


6x + 4y = 14
6x + 9y = 24


Now subtract the equations. I will subtract the second equation from the first so we don't get negative numbers (no one wants negative numbers if they can avoid them!):


6x + 9y = 24
6x + 4y = 14
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5y = 10
y = 2
Now substitute for y in one of the equations:
2x + 3(2)= 8


2x+6=8


2x=2
x=1

Checking our answer using the OTHER equation (very important so you don't make the same mistake twice!):
3(1)+2(2) = 7


3+4=7
7=7
We're good!
So the answer is:
x=1, y=2
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