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How do you solve $x - 2 y = 10$ $x - 2y = 10$ and $\frac{1}{2} x - 2 y = 4$ $1/2x - 2y = 4$ using substitution?

1 Answer

May 11, 2016

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

Explanation:

Given
[1] $XXX x - 2 y = 10$ $color(white)("XXX")x-2y=10$
[2] $XXX \frac{1}{2} x - 2 y = 4$ $color(white)("XXX")1/2x-2y=4$

We can rearrange [1] to give us an equation in terms of just $x$ $x$
[3] $XXX x = 2 y + 10$ $color(white)("XXX")x=2y+10$

This allows us to substitute $(2 y + 10)$ $(2y+10)$ for $x$ $x$ in [2]
[4] $XXX \frac{1}{2} (2 y + 10) - 2 y = 4$ $color(white)("XXX")1/2(2y+10)-2y=4$

Simplifying
[5] $XXX y + 5 - 2 y = 4$ $color(white)("XXX")y+5-2y=4$

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

[7] $XXX y = 1$ $color(white)("XXX")y=1$

Now we can substitute $1$ $1$ for $y$ $y$ back in [1]
[8] $XXX x - 2 (1) = 10$ $color(white)("XXX")x-2(1)=10$

Simplifying
[9] $XXX x = 12$ $color(white)("XXX")x=12$

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