Two lines have the same slope but different y-intercepts. How many solutions does the system have?

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Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

Multiple Choice

Two lines have the same slope but different y-intercepts. How many solutions does the system have?

Explanation:
When two lines share the same slope, they are parallel. If their y-intercepts are different, they are two distinct parallel lines that do not cross each other. A solution to the system would be a point where both lines meet, but there isn’t one here. So there are no solutions. For contrast: if the lines crossed once, there would be one solution; if they were the same line, there would be infinitely many solutions.

When two lines share the same slope, they are parallel. If their y-intercepts are different, they are two distinct parallel lines that do not cross each other. A solution to the system would be a point where both lines meet, but there isn’t one here. So there are no solutions. For contrast: if the lines crossed once, there would be one solution; if they were the same line, there would be infinitely many solutions.

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