Question

Find the condition that the system of equations $ax+by=c$ and $lx+my=n$ has a unique solution?

• A. $am=bl$
• B. $am\ne bl$
• C. $\frac{a}{m}\ne \frac{b}{n}$
• D. $ab=mn$

Answer 1

Answer: (B)

$am\ne bl$

The given equations are $ax+by=c$

or $ax+by-c=0$ and

$lx+my=n$

or $lx+my-n=0$.

The equations have a unique solution.

So, $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

Here $a_1=a,a_2=l,b_1=b,b_2=m,c_1=-c,c_2=-n$

$\therefore \frac{a_1}{a_2}=\frac{a}{l},\frac{b_1}{b_2}=\frac{b}{m}.$

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

$\Rightarrow am\ne bl.$

This is the required condition.