Question

For what value of ෺, the following system of equations will be inconsistent?

4x + 6y - 11 = 0

2x + ky - 7 = 0

Answer 1

The given system of equation may be written as

4x + 6y - 11 = 0

2x + 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 = 4, b_1 = 6, c_1 = -11`

And `a_2 = 2, b_2 = k, c_2 = -7`

For a unique solution, we must have

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

Now

`a_1/a_2 = b_1/b_2`

`=> 4/2 = 6/k`

`=> 4k = 12`

`=> k = 12/4 = 3`

Clearly, for this value of k, we have

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

Hence, the given system of equation is inconsistent, when k = 3