# How do you solve the following linear system:  2x-5y=-4, -3x-8y=-1, ?

Jul 15, 2016

$x = - 37$
$y = - 14$

#### Explanation:

$2 x - 5 y = - 4 \text{ } \left(1\right)$
$\textcolor{red}{3} \cdot \left(2 x - 5 y\right) = \textcolor{red}{3} \cdot \left(- 4\right)$
$6 x - 15 y = - 12$

$\textcolor{g r e e n}{6 x} = 15 y - 12 \text{ } \left(3\right)$

$- 3 x - 8 y = - 1 \text{ } \left(2\right)$
$\textcolor{red}{2} \left(- 3 x - 8 y\right) = \textcolor{red}{2} \left(- 1\right)$
$- 6 x = - 16 y - 2$

$\textcolor{g r e e n}{6 x} = 16 y + 2 \text{ } \left(4\right)$

$\text{we can write the equations (3) and (4) as equal}$

$15 y - 12 = 16 y + 2$
$- 12 - 2 = 16 y - 15 y$
$y = - 14$

$\text{now let us use (1) or (2)}$
$2 x - 5 \left(- 14\right) = - 4$
$2 x + 70 = - 4$
$2 x = - 70 - 4$
$2 x = - 74$
$x = - 37$