Q19 of 244 Page 157

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

The given two equations are:

2x + 3y – 1 = 0 …(i)

4x + ky – 10 = 0 …(ii)

Here, we have:

a1 = 2, b1 = 2 and c1 = – 1

a2 = 4, b2 = 6 and c2 = – 4

Now, we have

∴

Hence, the given system has no solution

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

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

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

Solve: and