📐 Mathematics · Straight Lines · JEE

If the line x/a + y/b = 1 passes through the intersection of 2x+3y=5 and x-2y=1 and is parallel to y=x, find a+b.

Answer: 1.

Correct answer: A. 1

Explanation: Solve 2x+3y=5, x-2y=1: x=11/7, y=3/7. Parallel to y=x means slope=1, so a=b. x/a + y/a = 1: (11/7+3/7)/a = 1, a = 2. a+b = 4. Wait: a = (11+3)/7 = 2. b = a = 2. a+b = 4.

The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.

Concept context

Points, lines, and curves on the Cartesian plane

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If the line x/a + y/b = 1 passes through the intersection of 2x+3y=5 and x-2y=1 and is parallel to y=x, find a+b.

Concept context

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