Question

If the pair of equations 3x + 2ky = 2 and 2x + 5y + 1 = 0 has no solution, then k = ______.

Answer 1

If the pair of equations 3x + 2ky = 2 and 2x + 5y + 1 = 0 has no solution, then k = `underlinebb(15/4)`.

Explanation:

Write the equations as 3x + 2ky – 2 = 0 and 2x + 5y + 1 = 0. 

For no solution (parallel distinct lines) we need `a_1/a_2 = b_1/b_2` but ≠ `c_1/c_2`.

Here a₁ = 3, b₁ = 2k, c1 = –2 and a₂ = 2, b₂ = 5, c₂ = 1.

So `3/2 = (2k)/5`

⇒ 15 = 4k

⇒ `k = 15/4`

Finally `c_1/c_2 = -2 ≠ 3/2`, so the lines are parallel and the system has no solution.