# How do solve the following linear system?:  x= y - 11 , x - 3y = 1 ?

Dec 31, 2015

$x = - 17$ and $y = - 6$

#### Explanation:

$x = y - 11$
$\implies y - x = 11$$\ldots \ldots \ldots \ldots \ldots \ldots \ldots \left(i\right)$
$x - 3 y = 1$$\ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \left(i i\right)$

By adding $\left(i\right)$ and $\left(i i\right)$, we have
$- 2 y = 12$
$\implies y = - 6$
Put $y = - 6$ in $\left(i i\right)$
$\implies x - 3 \left(- 6\right) = 1$
$\implies x + 18 = 1$
$\implies x = - 17$