Question

1. what indicates that a system of equations has no solution?

a. the lines are parallel
b. the lines have different slopes
c. the lines intersect
d. the lines are coincident

Explanation:

A system of linear equations has no solution when the graphs of the equations are parallel lines. Parallel lines have identical slopes but different y-intercepts, so they never intersect, meaning there is no shared (x,y) pair that satisfies both equations. Lines with different slopes (option b) intersect at exactly one point, giving one solution. Intersecting lines (option c) also have one solution. Coincident lines (option d) are the same line, so they have infinitely many solutions.

Answer:

a. The lines are parallel