Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `x + 2y = 8` and `x + 2y = -4`?

Answer 1

Intersecting graph lines are "consistent". Ones without any intersection (parallel) are "inconsistent".

Explanation:

Linear equations are "consistent" if they have a common point - a "solution". There can only be one point for linear equations, so by graphing them you just look for the point of intersection.

If there is NO intersection, there is no solution, and the system is "inconsistent". In this case, they must be parallel lines.

Set up a simple table of `x, y_1 and y_2` values. Plot them and look for the intersection. Set up the equations in similar form first.
`x + 2y = 8` `" "-> " "y = -1/2x + 4`
`x + 2y = -4` `" "->" " y = -1/2x - 2`

Of course, analytically we see that they have equal slopes, and thus are parallel. But, plot them to see the graphical representation anyway.