Two lines y = 2x + 3 and y = -x + 9 intersect at which coordinates?

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Prepare for the 8th Grade FAST Mathematics Test with our Pre-Algebra quiz. Study with multiple choice questions, each with hints and explanations. Build your confidence and ensure you're ready to excel!

Multiple Choice

Two lines y = 2x + 3 and y = -x + 9 intersect at which coordinates?

Explanation:
Intersections happen where two lines share a point, so the coordinates must make both line equations true at the same time. For these lines, y is given by 2x + 3 on the first and -x + 9 on the second. At the intersection these y-values are equal, so set 2x + 3 = -x + 9. Solve: 2x + 3 = -x + 9 → add x to both sides: 3x + 3 = 9 → subtract 3: 3x = 6 → x = 2. Now plug x = 2 into either equation to find y: y = 2(2) + 3 = 7, and the other equation gives y = -2 + 9 = 7, which matches. So the intersection is at (2, 7).

Intersections happen where two lines share a point, so the coordinates must make both line equations true at the same time. For these lines, y is given by 2x + 3 on the first and -x + 9 on the second. At the intersection these y-values are equal, so set 2x + 3 = -x + 9. Solve: 2x + 3 = -x + 9 → add x to both sides: 3x + 3 = 9 → subtract 3: 3x = 6 → x = 2. Now plug x = 2 into either equation to find y: y = 2(2) + 3 = 7, and the other equation gives y = -2 + 9 = 7, which matches. So the intersection is at (2, 7).

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