If am ≠ bl, then the system of equations


If am ≠ bl, then the system of equations

$a x+b y=c$

$l x+m y=n$

(a) has a unique solution

(b) has no solution

(c) has infinitely many solutions

(d) may or may not have a solution


Given $a m \neq b l$, the system of equations has

$a x+b y=c$

$l x+m y=n$

We know that intersecting lines have unique solution $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

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

Here $a_{1}=a, a_{2}=l, b_{1}=b, b_{2}=m$

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

$a \times m \neq l \times b$

Therefore intersecting lines, have unique solution

Hence, the correct choice is a

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now