How do solve the following linear system?: # 6x-4y=-1 , 3 x-y=4 #?

1 Answer
Jun 1, 2016

Given
[1]#color(white)("XXX")6x-4y=-1#
[2]#color(white)("XXX")3x-y=4#

Subtract 2 times [2] from [1]
[1]#color(white)("XXXxXX")6x-4y=-1#
#2xx#[2]#color(white)("XXX")underline(6x-2y=color(white)("X"x)8)#
[3]#color(white)("XXXXXxXX")-2y=-9#

Divide both sides of [3] by #(-2)#
[4]#color(white)("XXXXXXXXX")y=9/2#

Substitute #9/2# for #y# in [1]
[5]#color(white)("XXXXXX")6x-4(9/2)=-1#

Simplify
[6]#color(white)("XXXXXX")6x-18=-1#

[7]#color(white)("XXXXXX")6x=17#

[8]#color(white)("XXXXXX")x=17/6#

So the solution is #(x,y)=(17/6,9/2)#

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As always you should verify this result.

In this case substitute #17/6# for #x# and #9/2# for #y# in [2]

#color(white)("XXX")3x-y#

#color(white)("XXXXXX")=3(17/6)-9/2#

#color(white)("XXXXXX")=17/2-9/2#

#color(white)("XXXXXX")=8/2#

#color(white)("XXXXXX")=4# (which agrees with [2] so our work is valid)