Question

If the pair of straight lines $xy - x - y + 1 = 0$ and line $ax + 2y - 3 = 0$are concurrent, then a =

• A. – 1
• B. 0
• C. 3
• D. 1

Answer 1

Answer: (D)

1

Answer 2

Given that equation of pair of straight lines $xy - x - y + 1 = 0$ ⇒ $(x - 1)(y - 1) = 0$

⇒ $x - 1 = 0$ or $y - 1 = 0$

The intersection point of $x - 1 = 0,y - 1 = 0$is (1,1)

∴ Lines $x - 1 = 0,y - 1 = 0$and $ax + 2y - 3 = 0$are concurrent.

∴ The intersecting points of first two lines satisfy the third line. Hence, $a + 2 - 3 = 0$⇒ $a = 1$