Question

If you get an identity when trying to solve a system of two linear equations, the system's graph

must be
a) two parallel lines
b) two lines that are the same
c) two intersecting lines
d) two perpendicular lines
e) None of the above

Answer 1

a) two parallel lines

Explanation:

Two parallel lines have the same slope

Let's take a concrete example:
y = 2x + 4 (slope =2, y-intercept = 4)
y = 2x + 10 (slope = 2, y-intercept = 10)

Lines are parallel to each other

If you try to solve this equation you get

2x + 4 = 2x + 10

Subtracting 2x on both sides gives you the identity 4 = 10 (a contradiction)

This means the 2 line equations are inconsistent