# How do solve the following linear system?:  5x+2y=2, 3x - y = -6 ?

Nov 24, 2015

$\left(- \frac{10}{11} , \frac{36}{11}\right)$

#### Explanation:

Multiply the second equation by $2$.

$\left\{\begin{matrix}5 x + 2 y = 2 \\ 6 x - 2 y = - 12\end{matrix}\right.$

$11 x = - 10$

color(blue)(x=-10/11

Plug the newfound value for $x$ in to either equation to determine $y$.

$5 x + 2 y = 2 \implies 5 \left(\textcolor{b l u e}{- \frac{10}{11}}\right) + 2 y = 2$

$- \frac{50}{11} + 2 y = \frac{22}{11}$

$2 y = \frac{72}{11}$

color(green)(y=36/11

Write the answers in an ordered pair: $\left(- \frac{10}{11} , \frac{36}{11}\right)$