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How do you solve the following system?: $- x - 8 y = 32, y = \frac{1}{2} x + 2$ $-x-8y=32, y= 1/2x +2$

1 Answer

Nov 21, 2015

$(x, y) = (- \frac{48}{5}, - \frac{14}{5})$ $(x,y)=(-48/5,-14/5)$

Explanation:

[1] $XXX - x - 8 y = 32$ $color(white)("XXX")-x-8y=32$
[2] $XXX y = \frac{1}{2} x + 2$ $color(white)("XXX")y=1/2x+2$

Substitute $(\frac{1}{2} x + 2)$ $(1/2x+2)$ from [2] for $y$ $y$ in [1]
[3] $XXX - x - 8 (\frac{1}{2} x + 2) = 32$ $color(white)("XXX")-x -8(1/2x+2) = 32$

Simplify
[4] $XXX - x - 4 x - 16 = 32$ $color(white)("XXX")-x-4x-16 = 32$

[5] $XXX - 5 x = 48$ $color(white)("XXX")-5x=48$

[6] $XXX x = - \frac{48}{5}$ $color(white)("XXX")x=-48/5$

Substitute $(- \frac{48}{5})$ $(-48/5)$ from [6] for $x$ $x$ in [2]
[7] $XXX y = \frac{1}{2} (- \frac{48}{5}) + 2$ $color(white)("XXX")y=1/2(-48/5) + 2$

Simplify
[8] $XXX y = - \frac{14}{5}$ $color(white)("XXX")y=-14/5$

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