Question

In the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

kx + 2y - 5 = 0

3x + y - 1 = 0

Answer 1

The given system of equation is

kx + 2y - 5 = 0

3x + y - 1 = 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 = k, b_1 = 2, c_1 = -5`

And `a_2 = 3, b_2 = 1, c_2 = -1`

For a unique solution, we must have

`a_1/a_2 != b_1/b_2`

`:. k/3 != 2/1`

`=>? k != 6`

So, the given system of equations will have a unique solution for all real values of k other than 6.