How do solve the following linear system?:  x + y = 2, y = 4x + 4 ?

Jan 25, 2016

You could use the "Substitution Method" to get
$\textcolor{w h i t e}{\text{XXX}} \left(x , y\right) = \left(- \frac{2}{5} , \frac{12}{5}\right)$

Explanation:

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

Substitute $4 x + 4$ for $y$ (from equation [2]) in equation [1]
[3]$\textcolor{w h i t e}{\text{XXX}} x + 4 x + 4 = 2$

Simplify equation [3]
[4]$\textcolor{w h i t e}{\text{XXX}} 5 x = - 2$

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

Substitute $\left(- \frac{2}{5}\right)$ for $x$ (from equation [5]) in equation [1]
[6]$\textcolor{w h i t e}{\text{XXX}} \left(- \frac{2}{5}\right) + y = 2$

Simplify
[7]$\textcolor{w h i t e}{\text{XXX}} y = \frac{12}{5}$