# How do you solve the system of equations 3x-2y=7 and x+3y=-5?

Feb 2, 2017

See the entire solution process below:

#### Explanation:

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

$x + 3 y = - 5$

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

$x + 0 = - 5 - 3 y$

$x = - 5 - 3 y$

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

$3 \left(- 5 - 3 y\right) - 2 y = 7$

$- 15 - 9 y - 2 y = 7$

$- 15 - 11 y = 7$

$\textcolor{red}{15} - 15 - 11 y = \textcolor{red}{15} + 7$

$0 - 11 y = 22$

$- 11 y = 22$

$\frac{- 11 y}{\textcolor{red}{- 11}} = \frac{22}{\textcolor{red}{- 11}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 11}}} y}{\cancel{\textcolor{red}{- 11}}} = - 2$

$y = - 2$

Step 3) Substitute $- 2$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

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

$x = - 5 - \left(- 6\right)$

$x = - 5 + 6$

$x = 1$

The solution is $x = 1$ and $y = - 2$