# How do you solve the following linear system:  2x + 3y = 2, x + 6y = 4, ?

Jun 22, 2016

(x,y)=color(green)(""(0,2/3))

#### Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 y = 2$
[2]$\textcolor{w h i t e}{\text{XXX}} x + 6 y = 4$

[1]$\times 2$
$\textcolor{w h i t e}{\text{XXX}}$[3]$\textcolor{w h i t e}{\text{XXX}} 4 x + 6 y = 4$

[3]$-$ [2]
$\textcolor{w h i t e}{\text{XXX}}$[4]$\textcolor{w h i t e}{\text{XXX}} 3 x = 0$

[4]$\div 3$
$\textcolor{w h i t e}{\text{XXX}}$[5]$\textcolor{w h i t e}{\text{XXX}} x = 0$

Substituting (from [5]) $0$ for $x$ in [2]
$\textcolor{w h i t e}{\text{XXX}}$[6]#color(white)("XXX")0+6y=4

[6]$\div 6$
$\textcolor{w h i t e}{\text{XXX}}$[7]$\textcolor{w h i t e}{\text{XXX}} y = \frac{2}{3}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For verification purposes, you should check this result by substituting
$x = 0$ and $y = \frac{2}{3}$ back into equation [1].