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If a system of two linear equations has no solution, what is true about the lines?

A. The two lines are perpendicular.
B. The two lines intersect but are not perpendicular.
C. The two lines are parallel.
D. The two equations graph the same line.

User Seti Net
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1 Answer

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Final answer:

A system of two linear equations with no solution indicates that the two lines are parallel and therefore do not intersect at any point.

Step-by-step explanation:

If a system of two linear equations has no solution, it means that the two lines represented by these equations do not intersect at any point. The correct answer to this situation is C. The two lines are parallel. This is because parallel lines have the same slope and will never meet, no matter how far they are extended in either direction. On the contrary, if the lines were perpendicular (option A), they would intersect at a 90° angle. If the lines intersected but were not perpendicular (option B), there would be a single solution to the system. Lastly, if the two equations graphed the same line (option D), there would be infinitely many solutions since every point on the line would satisfy both equations.

User Jordan H
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