# How do solve the following linear system?: -9x + 5y = 16 , x - 3y = -6 ?

May 10, 2016

The solution for the system of equations is:
color(blue)(x = (- 9 )/ 11

color(blue)(y = 19 / 11

#### Explanation:

$\textcolor{g r e e n}{- 9 x} + 5 y = 16$..............equation $\left(1\right)$

$x - 3 y = - 6$ , multiplying by $9$
$\textcolor{g r e e n}{9 x} - 27 y = - 54$............equation $\left(2\right)$

Solving by elimination:

Adding equations $1$ and $2 :$

$\cancel{\textcolor{g r e e n}{- 9 x}} + 5 y = 16$
$\cancel{\textcolor{g r e e n}{9 x}} - 27 y = - 54$

$- 22 y = - 38$

$y = \frac{- 38}{- 22}$

color(blue)(y = 19 / 11

Finding $x$ from equation $2 :$

$x - 3 y = - 6$

$x = - 6 + 3 y$

$x = - 6 + 3 \cdot \left(\frac{19}{11}\right)$

$x = - 6 + \frac{57}{11}$

$x = \frac{- 66 + 57}{11}$

color(blue)(x = (- 9 )/ 11