Question

Find the value of p so that the three lines 3 x + y – 2 = 0, px + 2 y – 3 = 0 and 2 x – y – 3 = 0 may intersect at one point.

Answer 1

The equation of given lines is,

3x+y−2=0 px+2y−3=0 2x−y−3=0

Solve the equations 3x+y−2=0 and 2x−y−3=0.

5x−5=0 5x=5 x=1

For x=1, value of y is given by,

2×1−y−3=0 y=2−3 =−1

The point of intersection is given by ( 1,−1 )

All the three lines intersect at one point; so the point ( 1,−1 ) satisfies the equation of line px+2y−3=0.

p×1+2×( −1 )−3=0 p−2−3=0 p−5=0 p=5

Thus, the value of p for the three lines 3x+y−2=0, px+2y−3=0, and 2x−y−3=0 is 5.