Question

iF am is not equal to bl, then the pair of equations ax+by=c; lx+my=n:
a. has a unique solution
b. has no solution
c. has infinitely many solution
d. may or may not have a solution

Answer 1

Hi friends

if AM is not equal to BL, then the pair of equations AX+BY=c; lx+my=n:
a. has a unique solution

thank you

Answer 2

If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.

Given,

Pair of lines represented by the equations

ax + by = c

lx + my = n

For unique solution

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

For infinite solutions

$\frac{a}{l } = \frac{b}{m} = \frac{c}{n}$

For no solution

$\frac{a}{l } = \frac{b}{m} \neq \frac{c}{n}$

Given,

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

This can be transformed into

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

Therefore, If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.