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How do solve the following linear system?: # y = 5x - 7, x= y - 11 x #?

1 Answer

Jun 30, 2016

#(x,y)=color(blue)(""(-1,-12))#

Explanation:

Given:
[1]#color(white)("XXX")y=5x-7#
[2]#color(white)("XXX")x=y-11x#

Using [1] we see we can substitute #(5x-7)# for #y# in [2]
[3]#color(white)("XXX")x=(5x-7)-11x#

then simplifying
[4]#color(white)("XXX")x=-6x-7#

[5]#color(white)("XXX")7x=-7#

[6]#color(white)("XXX")x=-1#

Now we can substitute #(-1)# for #x# back in [1]
[7]#color(white)("XXX")y=5*(-1)-7#

[8]#color(white)("XXX")y=-12#

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