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

May 13, 2017

It is inconsistent.

Explanation:

We can immediately see that we are dealing with two parallel lines. If you write them in the form:

$y = m x + c$

where $m =$slope and $c =$ y-intercept, you get:

${y}_{1} = - \frac{1}{2} x + 3$

and

${y}_{2} = - \frac{1}{2} x - 1$

so that both lines have the same slope $m = - \frac{1}{2}$ (same inclination), different y-intercept and will never meet each other!

Graphically: