How do solve the following linear system?: # x= y - 11 x, y = 4x + 4 #?

1 Answer
Alan P.
Jun 16, 2016

#(x,y)=color(green)(""(1/2,6))#

Explanation:

Given
[1]#color(white)("XXX")x=y-11x#
[2]#color(white)("XXX")y=4x+4#

There are several ways to solve this, but it seems to be set up for substitution;
so, substituting, from [2], #4x+4# for #y# in [1]
[3]#color(white)("XXX")x=4x+4-11x#

[4]#color(white)("XXX")8x=4#

[5]#color(white)("XXX")x=1/2#

then, substituting, #1/2# for #x# in [2]
[6]#color(white)("XXX")y=4*(1/2)+4#

[7]#color(white)("XXX")y=6#

(or course, as always, you should plug these values back into both original equations to verify your results)

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