Question

which of the following graphs shows a system of equations with no solution?

Explanation:

Step1: Recall solution condition for linear systems

A system of linear equations has no solution when the lines are parallel (same slope, different y - intercepts), so they never intersect.

Step2: Analyze each graph

• Graph A: The two lines intersect, so the system has a solution.
• Graph B: The two lines intersect, so the system has a solution.
• Graph C: The two lines intersect, so the system has a solution.
• Graph D (the bottom - left graph): The two lines are parallel (they have the same slope and different y - intercepts), so they will never intersect, meaning the system of equations has no solution.

Answer:

The bottom - left graph (Graph D)