How do you solve the following system: #3x-y=12, 5x+2y=20 #?

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Answer 1 · 2018-06-03T19:15:28

#x=4, y=0#

#3x-y=12#
#5x+2y=20#

We can start and find x by multiplying equation 1 by 2.

#2(3x-y=12)#
#5x+2y=20#

#6x-2y=24#
#5x+2y=20#

Now we can add both equations together and cancel the y' s.

#6x-2y=24#
#11x=44#

Therefore, x = 4.

Now, we can back-substitute x to solve for y.

#6(4)-2y=24#
#24-2y=24#
#-2y=0#
#y=1#

Our solution set is (4, 1) or x = 4 and y = 1