# How do solve the following linear system?:  x-2y = -3 , 5x - 3y = -29 ?

Apr 29, 2016

$x = - 7 , y = - 2$

#### Explanation:

$x - 2 y = - 3$
$5 x - 3 y = - 29$

Rearrange the first equation to get $x$ by itself on the left hand side
$x = 2 y - 3$

Then substitute for $x$ in the second equation.
$5 \left(2 y - 3\right) - 3 y = - 29$
$10 y - 15 - 3 y = - 29$
$7 y = - 29 + 15 = - 14$
$\therefore y = - 2$

Substituting back into the reformatted first equation gives
$x = 2 \left(- 2\right) - 3$

$\therefore x = - 7$