Q18 of 244 Page 157

Find k for which the system 2x + 3y – 5 = 0, 4x + ky – 10 = 0 has a infinite number of solution.

The given two equations are:

2x + 3y – 5 = 0 …(i)

4x + ky – 10 = 0 …(ii)

Here, we have:

a₁ = 2, b₁ = 3 and c₁ = – 5

a₂ = 4, b₂ = k and c₂ = – 10

We know that, for the system having a infinite number of solutions we must have

∴ k = 6

Hence, the value of k is 6

Find the value of k for which the system 3x + 5 = 0, kx + 10y = 0 has a nonzero solution.

Find k for which the system kx – y = 2 and 6x – 2y = 3 has a unique solution.

Show that the system 2x + 3y – 1 = 0, 4x + ky – 10 = 0 has no solution.

Find k for which the system x + 2y = 3 and 5x + ky + 7 = 0 is inconsistent.