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

Question:

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

$a x+b y=c$

$b x+m y=n$

Solution:

GIVEN:

$a x+b y=c$

$l x+m y=n$

To find: To determine the condition for the system of equation to have a unique equation

We know that the system of equations

$a_{1} x+b_{1} y=c_{1}$

$a_{2} x+b_{2} y=c_{2}$

For unique solution

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Here

$\frac{a}{l} \neq \frac{b}{m}$

$a m \neq b l$

Hence for $a m \neq b l$ the system of equation have unique solution.