Question

How many solutions does the system of equations below have?

y=x+2
y=x-1
A one
B two
С none
D infinitely many

Answer 1

C

Explanation:

Answer 2

C: none

Explanation:

Here we have two separate functions named 'y.' Eliminate 'y' temporarily by equating these functions together:

x + 2 = y = x - 1

Subtracting x from both sides, we get:

0 + 2 = y = 0 - 1, or

2 = -1

This is never true, so C is the correct answer: NO solutions.

An easier way in which to do this problem is to visualize the graphs of

y = x + 2 and y = x - 1. The graphs are parallel straight lines; they never intersect, and therefore we can conclude "no solution."