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
The Legend
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#
#-#
#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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