The line L1 passes through the point (0,2) and has slope –3. Find its intersection point with the line 2x+3y=5.

Step-by-step solution

1. Find equation of L1 using point–slope form: y−2 = –3(x−0) giving y = –3x + 2.
2. Solve the system {y = –3x + 2, 2x + 3y = 5}.
3. Substitute y from the first equation into the second: 2x + 3(–3x + 2) = 5.
4. Simplify: 2x – 9x + 6 = 5 → –7x + 6 = 5.
5. Solve for x: –7x = –1 → x = 1/7.
6. Find y: y = –3(1/7)+2 = –3/7 + 14/7 = 11/7.

Concept tested: Intersection of two lines.

Published 4 October 2026 · How this solution was prepared and checked