Question

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

• A. $an\ne cl$
• B. $am\ne bl$
• C. $bm\ne al$
• D. $bn\ne al$
• E. None of these

Answer 1

The correct option is B $am\ne bl$

We have, ax + by = c ...... (1)
lx + my = n ...... (2)
Here $a_1=a,b_1=b,c_1=c$
$a_2=1,b_2=m,c_2=n$
If the given system of linear equations has a unique solution,
$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\Rightarrow \frac{a}{l}\ne \frac{b}{m}\Rightarrow am\ne bl$