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)
