If two linear equations represent parallel lines, what is the solution to the system?

If two linear equations represent parallel lines, what is the solution to the system?

• A. The intersection point
• B. Infinite solutions
• C. One solution
• D. No solution

Answer: (D)

When solving a system by graphing, the solutions are the points where the lines intersect. If two linear equations represent parallel lines, they have the same slope but different intercepts, so they never cross. Since there is no point that satisfies both equations at once, the system has no solution. (If the lines were the same line, you’d have infinitely many solutions; if they intersect, you’d have exactly one solution.)

When solving a system by graphing, the solutions are the points where the lines intersect. If two linear equations represent parallel lines, they have the same slope but different intercepts, so they never cross. Since there is no point that satisfies both equations at once, the system has no solution. (If the lines were the same line, you’d have infinitely many solutions; if they intersect, you’d have exactly one solution.)