# How do solve the following linear system?: -4x + 9y = 9 , x - 3y = -6 ?

Dec 30, 2015

The solution for the system of equations is:

color(blue)(x=9 ,y=5

#### Explanation:

$\textcolor{b l u e}{- 4 x} + 9 y = 9$..........equation $\left(1\right)$

$x - 3 y = - 6$, multiplying by $4$
$\textcolor{b l u e}{4 x} - 12 y = - 24$.....equation $\left(2\right)$

Solving by elimination:

$\cancel{\textcolor{b l u e}{- 4 x}} + 9 y = 9$

$\cancel{\textcolor{b l u e}{4 x}} - 12 y = - 24$

$- 3 y = - 15$

$y = \frac{- 15}{- 3}$

color(blue)(y=5

Finding $x$ from equation $2$:
$x - 3 y = - 6$

$x = - 6 + 3 y$

$x = - 6 + 3 \times 5$

$x = - 6 + 15$

color(blue)(x =9