Find the intersection of the lines y = x + 1 and y = 3x - 5.

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Multiple Choice

Find the intersection of the lines y = x + 1 and y = 3x - 5.

Explanation:
Two lines intersect where their y-values are the same for the same x. Set the equations equal: x + 1 = 3x − 5. Solve for x: subtract x from both sides to get 1 = 2x − 5, then add 5 to get 6 = 2x, so x = 3. Substitute back to find y: y = x + 1 = 4. The intersection is (3, 4). Quick check: plugging x = 3 into the other equation gives y = 9 − 5 = 4, which matches. The other candidate points don’t satisfy both equations simultaneously.

Two lines intersect where their y-values are the same for the same x. Set the equations equal: x + 1 = 3x − 5. Solve for x: subtract x from both sides to get 1 = 2x − 5, then add 5 to get 6 = 2x, so x = 3. Substitute back to find y: y = x + 1 = 4. The intersection is (3, 4). Quick check: plugging x = 3 into the other equation gives y = 9 − 5 = 4, which matches. The other candidate points don’t satisfy both equations simultaneously.

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