Question

Obtain the condition for the following system of linear equations to have a unique solution
$ax+by=c$
$lx+my=n$

Answer 1

$ax+by=6lx+my=n$

Comparing $ax+by-c=0$

with $a_{1}x+b_{1}y+c_1=0a_1=a,b_1=b,c_1=-c$

Comparing $lx+my-n=0$

with $a_{2}x+b_{2}y+c_2=0$

$a_2=l,b_2=m,c_2=-n.$

$\therefore$ For a unique solution ,

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\Rightarrow \frac{a}{l}\ne \frac{b}{m}\Rightarrow am\ne bl$