Question

Obtain the condition for the following system of linear equations to have a unique solution

ax + by = c

lx + my = n

Answer 1

The given system of equations may be written as

ax + by − c = 0

lx + my − n = 0

It is of the form

`a_1x + b_1y + c_1 = 0`

`a_2x + b_2y + c_2 = 0`

Where `a_1 = a, b_1 = b, c_1 = -c`

And `a_2 = l, b_2 = m,c_2 = -n`

For unique solution, we must have

`a_1/a_2 != b_1/b_2`

`=> a/l != b/m`

`=> am != bl`

Hence, `am != bl` is the required condition.