Question

Find the value of k for which the following system of equations has a unique solution:

x + 2y = 3

5x + ky + 7 = 0

Answer 1

The given system of equation is

x + 2y - 3 = 0

5x + ky + 7 = 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 = 1,b_1 = 2,c_1 = -3`

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

For a unique solution, we must have

`a_1/a_2 != b_1/b_2`

`:. 1/5 != 2/k`

`=> k != 10`

So, the given system of equations will have a unique solution for all real values of k other than 10.