# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent y = -x - 4 and y = x + 2?

May 29, 2017

See a solution process below:

#### Explanation:

Step 1) Because the first equation is already solved for $y$ we can substitute $\left(- x - 4\right)$ from $y$ in the second equation and solve for $x$:

$y = x + 2$ becomes:

$- x - 4 = x + 2$

$\textcolor{red}{x} - x - 4 - \textcolor{b l u e}{2} = \textcolor{red}{x} + x + 2 - \textcolor{b l u e}{2}$

$0 - 6 = \textcolor{red}{1 x} + 1 x + 0$

$- 6 = 2 x$

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

$- 3 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}}$

$- 3 = x$

$x = - 3$

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

$y = - x - 4$ becomes:

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

$y = 3 - 4$

$y = - 1$

The solution is: $x = - 3$ and $y = - 1$ or $\left(- 3 , - 1\right)$