How do you solve the following system?: # x + 3-2y=7 , x=-3x + 4y-17 #

1 Answer
Alan P.
Mar 15, 2018

#(x,y)=(-25/2,-33/4)#

Explanation:

Given
[1]#color(white)("XXX")x+3-2y=7#
[2]#color(white)("XXX")x=-3x+4y-17#

Re-arrange [1] and [2] into standard form to get (respectively)
[3]#color(white)("XXX")x-2y=4#
[4]#color(white)("XXX")4x-4y=-17#

Since this was asked under "Systems Using Substitution"
Re-write [3] as #x# in terms of #y#
[5]#color(white)("XXX")x=2y+4#

Then substitute #(2y+4)# for #x# in [4]
[6]#color(white)("XXX")4(2y+4)-4y=-17#

Simplifying
[7]#color(white)("XXX")8y+16-4y=-17#

[8]#color(white)("XXX")4y=-33#

[9]#color(white)("XXX")y=-33/4#

Substituting #(-33/4)#for #y# in [3]
[10]#color(white)("XXX")x-2(-33/4)=4#

Simplifying
[11]#color(white)("XXX")x+33/2=8/2#

[12]#color(white)("XXX")x=-25/2#

[These values may look a bit ugly, but substituting back into equations [1] and [2] verify that they are correct.]

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