Question

2x + y = 2
graph to determine.
the only solution is (0,0).
the only solution is (0,2).
there are an infinite number of solutions.
there is no solution

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange $2x + y = 2$ to $y = -2x + 2$.

Step2: Identify solution nature

This is a linear equation in two variables. Every point $(x, y)$ that satisfies $y = -2x + 2$ is a solution, and there are infinitely many such points.

Answer:

There are an infinite number of solutions.