are these two systems CONSISTENT or INCONSISTENT? y = 2x + 5-2x + y = -2

Question

Consistent or inconsistent?

y = 2x + 5
-2x + y = -2

Answer 1

Inconsistent - you'll see this by solving for values of x and y. Start by substituting the first equation for y into the second:

-2x + 2x + 5 = -2

-2x + 2x = -7

The -2x and +2x cancel out, leaving 0 = -7, which isn't true, so you know the system is inconsistent.

Hope that helps!

Katherine P.