Question

the two lines graphed below are parallel. how many solutions are there to the system of equations? a. zero b. one c. two d. infinitely many

Explanation:

Step1: Recall solution definition

A solution to a system of linear equations is a point \((x,y)\) that satisfies both equations, which is the intersection point of their graphs.

Step2: Analyze parallel lines

Parallel lines have the same slope and never intersect (by definition of parallel lines in a plane).

Step3: Determine number of solutions

Since the two lines are parallel and never intersect, there are no points that satisfy both equations. So the number of solutions is zero.

Answer:

A. Zero