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

Jun 30, 2016

Answer:

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

Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} y = 5 x - 7$
[2]$\textcolor{w h i t e}{\text{XXX}} x = y - 11 x$

Using [1] we see we can substitute $\left(5 x - 7\right)$ for $y$ in [2]
[3]$\textcolor{w h i t e}{\text{XXX}} x = \left(5 x - 7\right) - 11 x$

then simplifying
[4]$\textcolor{w h i t e}{\text{XXX}} x = - 6 x - 7$

[5]$\textcolor{w h i t e}{\text{XXX}} 7 x = - 7$

[6]$\textcolor{w h i t e}{\text{XXX}} x = - 1$

Now we can substitute $\left(- 1\right)$ for $x$ back in [1]
[7]$\textcolor{w h i t e}{\text{XXX}} y = 5 \cdot \left(- 1\right) - 7$

[8]$\textcolor{w h i t e}{\text{XXX}} y = - 12$