# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent x – 2y = 8 and x + y = –1?

Jul 6, 2017

See a solution process below:

#### Explanation:

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

$x - 2 y = 8$

$x - 2 y + \textcolor{red}{2 y} = 8 + \textcolor{red}{2 y}$

$x - 0 = 8 + 2 y$

$x = 8 + 2 y$

Step 2) Substitute $\left(8 + 2 y\right)$ for $x$ in the second equation and solve for $y$:

$x + y = - 1$ becomes:

$\left(8 + 2 y\right) + y = - 1$

$8 + 2 y + 1 y = - 1$

$8 + \left(2 + 1\right) y = - 1$

$8 + 3 y = - 1$

$- \textcolor{red}{8} + 8 + 3 y = - \textcolor{red}{8} - 1$

$0 + 3 y = - 9$

$3 y = - 9$

$\frac{3 y}{\textcolor{red}{3}} = - \frac{9}{\textcolor{red}{3}}$

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

$y = - 3$

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

$x = 8 + 2 y$ becomes:

$x = 8 + \left(2 \cdot - 3\right)$

$x = 8 + \left(- 6\right)$

$x = 2$

The solution is: $x = 2$ and $y = - 3$ or $\left(2 , - 3\right)$

Because there is at least one point in common these equations are consistent.