# How do you solve the following system?: -9x -8y =-3, 2x -2y = -4

Feb 12, 2016

The solution for the system of equations is:
color(green)(x = -13 / (17)

color(green)(y =21/17

#### Explanation:

$- 9 x - \textcolor{b l u e}{8 y} = - 3$.......equation $\left(1\right)$

$2 x - 2 y = - 4$, multiplying this equation by $4$
$8 x - \textcolor{b l u e}{8 y} = - 16$..........equation $\left(2\right)$

Solving by elimination

Subtracting equation $2$ from $1$:

$- 9 x - \cancel{\textcolor{b l u e}{8 y}} = - 3$
$- 8 x + \cancel{\textcolor{b l u e}{8 y}} = 16$

$- 17 x = 13$

color(green)(x = -13 / (17)

Finding $y$ from equation $1$

$- 9 x - \textcolor{b l u e}{8 y} = - 3$

$- 9 x + 3 = 8 y$

$- 9 \times \textcolor{g r e e n}{- \frac{13}{17}} + 3 = 8 y$

$\frac{117}{17} + 3 = 8 y$

$\frac{117}{17} + \frac{51}{17} = 8 y$

$\frac{168}{17} = 8 y$

$y = \frac{168}{17 \times 8}$

color(green)(y =21/17