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

1 Answer

Jun 16, 2016

$(x, y) = (\frac{1}{2}, 6)$ $(x,y)=color(green)(""(1/2,6))$

Explanation:

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

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

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

[5] $XXX x = \frac{1}{2}$ $color(white)("XXX")x=1/2$

then, substituting, $\frac{1}{2}$ $1/2$ for $x$ $x$ in [2]
[6] $XXX y = 4 \cdot (\frac{1}{2}) + 4$ $color(white)("XXX")y=4*(1/2)+4$

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

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

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