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#?

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Answer 1 · 2017-05-13T20:29:34

It is inconsistent.

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

#y=mx+c#

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

#y_1=-1/2x+3#

and

#y_2=-1/2x-1#

so that both lines have the same slope #m=-1/2# (same inclination), different y-intercept and will never meet each other!

Graphically:

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