Question

For what value of k, the system of equations x+y-4=0 and 2x+ky-3=0 has no solution.

Answer 1

We have x+y = 4 (1)
2x+ky = 3 (2)
Multiply equation (1) by 2 to get
2x+2y = 8 (3)
Now if k = 2, then we will have
2x+2y = 3 (4) from (2)
while (3) says 2x+2y = 8
which is inconistsent with (4) so there will be no solution.
Hence if k = 2, there is no solution Answer