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

1 Answer

Jun 30, 2016

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

Explanation:

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

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

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

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

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

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

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

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