Question

Find the value of k for which each of the following system of equations have no solution :

2x + ky = 11
5x − 7y = 5

Answer 1

The given system of equation is

2x + ky - 11 =0

5x − 7y - 5 = 0

The system of equation is of the form

`a_1x + b_1y + c_1 = 0`

`a_2x + b_2y + c_2 = 0`

Where, `a_1 = 2,b_1 = k, c_1 = -11`

And `a_2 = 5, b_2 = -7, c_2 = -5`

For a unique solution, we must have

`a_1/a_2 - b_1/b_2 != c_1/c_2`

`=> 2/5 = k/(-7) != (-11)/(-5)`

Now

`2/5 = k/(-7)`

`=> 2 xx (-7) = 5k`

`=> 5k = -14`

`=> k = (-14)/5`

Cleary for `(-14)/5` we have `k/(-7) != (-11)/(-5)`

Hence, the given system of equation will have no solution if `k = (-14)/5`