# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 2x + 2y = –6 and 3x – 2y = 11?

Sep 4, 2017

See a solution process below:

#### Explanation:

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

$2 x + 2 y = - 6$

$2 x + 2 y - \textcolor{red}{2 y} = - 6 - \textcolor{red}{2 y}$

$2 x + 0 = - 6 - 2 y$

$2 x = - 6 - 2 y$

$\frac{2 x}{\textcolor{red}{2}} = \frac{- 6 - 2 y}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = \frac{- 6}{\textcolor{red}{2}} - \frac{2 y}{\textcolor{red}{2}}$

$x = - 3 - y$

Step 2) Substitute $\left(- 3 - y\right)$ for $x$ in the second equation and solve for $y$:

$3 x - 2 y = 11$ becomes:

$3 \left(- 3 - y\right) - 2 y = 11$

$\left(3 \times - 3\right) - \left(3 \times y\right) - 2 y = 11$

$- 9 - 3 y - 2 y = 11$

$- 9 - 5 y = 11$

$\textcolor{red}{9} - 9 - 5 y = \textcolor{red}{9} + 11$

$0 - 5 y = 20$

$- 5 y = 20$

$\frac{- 5 y}{\textcolor{red}{- 5}} = \frac{20}{\textcolor{red}{- 5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} y}{\cancel{\textcolor{red}{- 5}}} = - 4$

$y = - 4$

Step 3) Substitute $- 4$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = - 3 - y$ becomes:

$x = - 3 - \left(- 4\right)$

$x = - 3 + 4$

$x = 1$

The Solution Is: $x = 1$ and $y = - 4$ or $\left(1 , - 4\right)$