Question

1. a system of equations has no solution. what does this mean about the graphs?

a. the lines intersect once.
b. the lines are parallel.
c. the lines overlap completely.
d. the lines form a right angle.
a
b
c
d

Explanation:

A system of linear equations has no solution when there is no point that satisfies all equations simultaneously. Parallel lines have identical slopes but different y-intercepts, so they never intersect, meaning there is no common solution. Intersecting lines (A) have one solution, overlapping lines (C) have infinitely many solutions, and perpendicular lines (D) intersect at a right angle, having one solution.

Answer:

B. The lines are parallel.