# How do you solve the system x=-4y and 3x+2y=20 using substitution?

Oct 15, 2016

$\left(x , y\right) = \left(8 , - 2\right)$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{x} = \textcolor{red}{- 4 y}$
and
$\textcolor{w h i t e}{\text{XXX}} 3 \textcolor{red}{x} + 2 y = 20$

Substituting color(red)(""(-4y)) for $\textcolor{red}{x}$ into the second equation:
$\textcolor{w h i t e}{\text{XXX")3 * color(red)(} \left(- 4 y\right)} + 2 y = 20$

$\textcolor{w h i t e}{\text{XXX}} - 12 y + 2 y = 20$

$\textcolor{w h i t e}{\text{XXX}} - 10 y = 20$

$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{y} = \textcolor{b l u e}{- 2}$

Now substitute color(blue)(""(-2)) for $\textcolor{b l u e}{y}$ back in the original equation $x = - 4 \textcolor{b l u e}{y}$

$\textcolor{w h i t e}{\text{XXX")x=-4 * color(blue)(} \left(- 2\right)}$

$\textcolor{w h i t e}{\text{XXX}} x = 8$