Question:
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
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
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