# How do solve the following linear system?:  x+2y=1 , 4 x+ 16y = 2 ?

##### 1 Answer
Dec 8, 2015

$\left(x , y\right) = \left(\frac{3}{2} , - \frac{1}{4}\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} x + 2 y = 1$
[2]$\textcolor{w h i t e}{\text{XXX}} 4 x + 16 y = 2$

Multiply [1] by $4$ to generate the same $x$ coefficient as in [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 4 x + 8 y = 4$

Subtract [3] from [2]
[4]$\textcolor{w h i t e}{\text{XXX}} 8 y = - 2$

Divide both sides of [4] by $8$
[5]$\textcolor{w h i t e}{\text{XXX}} y = - \frac{1}{4}$

Substitute $\left(- \frac{1}{4}\right)$ for $y$ in [2]
[6]$\textcolor{w h i t e}{\text{XXX}} 4 x + 16 \cdot \left(- \frac{1}{4}\right) = 2$

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

Add $4$ to both sides
[8]$\textcolor{w h i t e}{\text{XXX}} 4 x = 6$

Divide both sides of [8] by $4$
[9]$\textcolor{w h i t e}{\text{XXX}} x = \frac{3}{2}$