# How do you solve the system of equations: -3x-3y=3 and y=-5x-17?

Apr 24, 2018

When solved by substitution:

$x = - 4$
$y = 3$

#### Explanation:

Let

$- 3 x - 3 y = 3$

be eqn $\left(1\right)$ and let

$y = - 5 x - 17$

be eqn $\left(2\right)$. By means of substitution, we substitute eqn $\left(2\right)$ into eqn $\left(1\right)$ to find the unknown, $x$.

We arrive at:

$- 3 x - 3 \left(- 5 x - 17\right) = 3$

$- 3 x + 15 x + 51 = 3$

$15 x - 3 x = 3 - 51$

$12 x = - 48$

$x = \frac{- 48}{12}$

$x = - 4$

We now have the value of $x$, hence we can substitute $x = - 4$ in eqn $\left(2\right)$ to find the unknown $y$. By doing this, we arrive at:

$y = - 5 \left(- 4\right) - 17$

$y = 20 - 17$

$y = 3$

Hence $x = - 4 \mathmr{and} y = 3$.

But to be sure, always double-check your work by replacing your values in the equations to see if they make the equations true.

$- 3 \left(- 4\right) - 3 \left(3\right) = 3$
$12 - 9 = 3 \to$ true

$3 = - 5 \left(- 4\right) - 17$
$3 = 20 - 17 \to$ true

The values of $x$ and $y$ make the equations true, hence $x = - 4$ and $y = 3$.