#### Question

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

ax + by = c

lx + my = n

#### Solution

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 = 1, b_1 = 2, 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.

Is there an error in this question or solution?

#### APPEARS IN

Solution Obtain the Condition for the Following System of Linear Equations to Have a Unique Solution Ax + By = C Lx + My = N Concept: Pair of Linear Equations in Two Variables.