How do solve the following linear system?: # 3x – 4y = 7, x-y=2 #?

1 Answer
Alan P.
May 16, 2018

#(x,y)=(+1,-1)#

Explanation:

Given
[1]#color(white)("XXX")3x-4y=7#
[2]#color(white)("XXX")x-y=2#

There are several ways to solve this but since it was asked under "Systems Using Substitution", we will approach it that way:

Rearrange [2] into an equation in terms of #x#
[3]#color(white)("XXX")x=y+2#

Now substitute #(y+2)# for #x# in [1]
[4]#color(white)("XXX")3(y+2)-4y=7#

Expanding and simplifying [4]
[5]#color(white)("XXX")-y+6=7#
or
[6]#color(white)("XXX")y=-1#

Now substitute #(-1)# for #y# back in [2] (or you could have used [1])
[7]#color(white)("XXX")x-(-1)=2#
Simplifying:
[8]#color(white)("XXX")x=1#

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