# How do you solve  x+5y=-3 and 3x-2y=8 using substitution?

Feb 12, 2017

See the entire simplification process below:

#### Explanation:

Step 1) Solve the first equation for $x$:

$x + 5 y = - 3$

$x + 5 y - \textcolor{red}{5 y} = - 3 - \textcolor{red}{5 y}$

$x + 0 = - 3 - 5 y$

$x = - 3 - 5 y$

Step 2) Substitute $- 3 - 5 y$ for $x$ in the second equation and solve for $y$:

$3 x - 2 y = 8$ becomes:

$3 \left(- 3 - 5 y\right) - 2 y = 8$

$\left(3 \times - 3\right) - \left(3 \times 5 y\right) - 2 y = 8$

$- 9 - 15 y - 2 y = 8$

$- 9 - 17 y = 8$

$\textcolor{red}{9} - 9 - 17 y = \textcolor{red}{9} + 8$

$0 - 17 y = 17$

$- 17 y = 17$

$\frac{- 17 y}{\textcolor{red}{- 17}} = \frac{17}{\textcolor{red}{- 17}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 17}}} y}{\cancel{\textcolor{red}{- 17}}} = - 1$

$y = - 1$

Step 3) Substitute $- 1$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = - 3 - 5 y$ becomes:

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

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

$x = - 3 + 5$

$x = 2$

The solution is: $x = 2$ and $y = - 1$ or $\left(2 , - 1\right)$