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

Jun 16, 2016

(x,y)=color(green)(""(1/2,6))

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} x = y - 11 x$
[2]$\textcolor{w h i t e}{\text{XXX}} y = 4 x + 4$

There are several ways to solve this, but it seems to be set up for substitution;
so, substituting, from [2], $4 x + 4$ for $y$ in [1]
[3]$\textcolor{w h i t e}{\text{XXX}} x = 4 x + 4 - 11 x$

[4]$\textcolor{w h i t e}{\text{XXX}} 8 x = 4$

[5]$\textcolor{w h i t e}{\text{XXX}} x = \frac{1}{2}$

then, substituting, $\frac{1}{2}$ for $x$ in [2]
[6]$\textcolor{w h i t e}{\text{XXX}} y = 4 \cdot \left(\frac{1}{2}\right) + 4$

[7]$\textcolor{w h i t e}{\text{XXX}} y = 6$

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