# How do solve the following linear system?:  x= y - 11 , 8x + 3y= -9 ?

Jan 5, 2016

$x = - \frac{42}{11} \mathmr{and} y = \frac{79}{11}$

#### Explanation:

$x = y - 11$
$\implies x - y = - 11. \ldots \ldots \ldots \ldots . . \left(i\right)$
$8 x + 3 y = - 9. \ldots \ldots . \left(i i\right)$
Multiply $\left(i\right)$ by $3$ and add in $\left(i i\right)$
$\implies 3 x - 3 y = - 33$
$+ 8 x + 3 y = - 9$
By addition we have
$11 x = - 42$
$\implies x = - \frac{42}{11}$
Put $x = - \frac{42}{11}$ in $\left(i\right)$
$\implies - \frac{42}{11} - y = - 11$
$\implies - 42 - 11 y = - 121$
$\implies 11 y = 79$
$\implies y = \frac{79}{11}$