# How do you solve the following system?:  8x - 2y = - 4 , -4x + 2y = 2

Mar 24, 2018

$\left(x , y\right) \to \left(- \frac{1}{2} , 0\right)$

#### Explanation:

$8 x \textcolor{red}{- 2 y} = - 4 \to \left(1\right)$

$- 4 x \textcolor{red}{+ 2 y} = 2 \to \left(2\right)$

$\text{adding equations "(1)" and "(2)" eliminates the y-term}$

$\left(1\right) + \left(2\right) \text{ term by term on both sides}$

$\left(8 x - 4 x\right) + \left(- 2 y + 2 y\right) = \left(- 4 + 2\right)$

$\Rightarrow 4 x = - 2$

$\text{divide both sides by 2}$

$\frac{\cancel{4} x}{\cancel{4}} = \frac{- 2}{4}$

$\Rightarrow x = - \frac{1}{2}$

$\text{substitute "x=-1/2" into either of the 2 equations}$

$\left(2\right) \Rightarrow 2 + 2 y = 2$

$\Rightarrow 2 y = 2 - 2 = 0 \Rightarrow y = 0$

$\text{the solution is } \left(x , y\right) \to \left(- \frac{1}{2} , 0\right)$