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

1 Answer
Alan P.
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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