# How do solve the following linear system?:  x - 3y = 8 , 3y = 15 -6x ?

Dec 5, 2015

The solution for the system of equations is :

color(blue)(x=23/7, y=(-11)/7

#### Explanation:

$x - 3 y = 8$

x=color(blue)(8 +3y....................equation $1$

$3 y = 15 - 6 x$................equation $2$

Solving by substitution.

Substituting equation $1$ in $2$

$3 y = 15 - 6 x$

$3 y = 15 - 6 \cdot \left(\textcolor{b l u e}{8 + 3 y}\right)$

$3 y = 15 - 48 - 18 y$

$3 y + 18 y = 15 - 48$

$21 y = - 33$

$y = \frac{- \cancel{33}}{\cancel{21}}$

color(blue)(y=(-11)/7

Now, we substitute this value of $y$ in equation $1$ to find $x$

$x = 8 + 3 y$

$x = 8 + 3 \cdot \left(- \frac{11}{7}\right)$

$x = 8 - \frac{33}{7}$

$x = \frac{56}{7} - \frac{33}{7}$

color(blue)(x=23/7