# How do you solve the following system?: 9y = -3x - 9 , 5x + 3y = -3

Apr 7, 2018

Substitution/Elimination/Graphing Method

#### Explanation:

Using the substitution method, starting with the first equation:

$9 y = - 3 x - 9$

$9 y + 9 = - 3 x$

$\frac{9 y}{-} 3 + \frac{9}{-} 3 = \frac{- 3 x}{-} 3$

$x = - 3 y - 3$

Substituting $\left(x = - 3 y - 3\right)$ into the second equation to find $y$:

$5 x + 3 y = - 3$

$5 \left(- 3 y - 3\right) + 3 y = - 3$

$- 15 y - 15 + 3 y = - 3$

$- 12 y = 12$

$y = - 1$

Now substituting $\left(y = - 1\right)$ into second equation to find $x$:

$5 x + 3 y = - 3$

$5 x + 3 \left(- 1\right) = - 3$

$5 x - 3 = - 3$

$5 x = 0$

$x = 0$

Test $\left(x = 0 , y = - 1\right)$ in other equation to validate

$9 y = - 3 x - 9$

$9 \left(- 1\right) = - 3 \left(0\right) - 9$

$- 9 = - 9$,