# How do solve the following linear system?:  -6x+6y=6 , x+2y=5 ?

May 6, 2018

$x = 1 \mathmr{and} y = 2$

#### Explanation:

$\textcolor{w h i t e}{\times \times x} - 6 x + 6 y = 6 \text{ } \ldots . A$
$\textcolor{w h i t e}{\times \times \times \times} \textcolor{b l u e}{x} + 2 y = 5 \text{ } \ldots . B$
$A \div 6 \rightarrow \textcolor{b l u e}{- x} + y = 1 \text{ } \ldots . C$

we now have a perfect scenario where $\textcolor{b l u e}{x} \mathmr{and} \textcolor{b l u e}{- x}$ are additive inverses. Their sum is $0$
Add the equations $A \mathmr{and} C$ together.

$A + C \rightarrow \textcolor{w h i t e}{\times \times} 3 y = 6$
$\textcolor{w h i t e}{\times \times \times \times \times \times} y = 2$

Substitute into $B : \text{ } x + 2 \left(2\right) = 5$
$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times} x = 1$

Check in $C$

$\left(- 1\right) + \left(2\right) = 1 \text{ } \ldots . C$