Question

If $am\ne bl$, then the system of equations $ax+by=c$ and $lx+my=n$ has:

• A. A unique solution
• B. No solution
• C. Infinitely many solutions
• D. May or may not have a solution

Answer 1

The correct option is A A unique solution

Given that $am\ne bl$

$\Rightarrow \frac{a}{l}\ne \frac{b}{m}$

We know that if $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$

is a pair of linear equations in two variables $x$ and $y$ such that

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$, then the pair of linear equations is consistent with unique solution.

Hence, given pair of equations has a unique solution.