# How do you solve the following system:  5x+8y= -29, 5x-9y=-2 ?

Feb 13, 2016

The solution for the system of equations is:
$x = - \frac{277}{85}$

$y = - \frac{27}{17}$

#### Explanation:

$\textcolor{b l u e}{5 x} + 8 y = - 29$ ......equation $\left(1\right)$
$\textcolor{b l u e}{5 x} - 9 y = - 2$.........equation $\left(2\right)$

Solving by elimination

Subtracting equation $2$ from $1$

$\cancel{\textcolor{b l u e}{5 x}} + 8 y = - 29$
$- \cancel{\textcolor{b l u e}{5 x}} + 9 y = 2$

$17 y = - 27$

$y = - \frac{27}{17}$

Finding $x$ from equation $1$

$5 x + 8 y = - 29$

$5 x + 8 \times \left(- \frac{27}{17}\right) = - 29$

$5 x + \left(- \frac{216}{17}\right) = - 29$

$5 x = - 29 + \frac{216}{17}$

$5 x = - \frac{493}{17} + \frac{216}{17}$

$5 x = - \frac{277}{17}$

$x = - \frac{277}{17 \times 5}$

$x = - \frac{277}{85}$