Question

For which values of 'a' and 'b' does the following pair of linear equations have infinite number of solutions -
$2x+3y=7,(a-b)x+(a+b)y=3a+b-2$

• A. $a=5,b=1$
• B. $a=4,b=2$
• C. $a=1,b=5$
• D. $a=2,b=4$

Answer 1

Answer: (A)

$a=5,b=1$

we have, $2x+3y=7$ and $(a-b)x+(a+b)y=3a+b-2$

For infinite solution

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

$\frac{2}{a-b}=\frac{3}{a+b}=\frac{7}{3a+b-2}$

$\Rightarrow \frac{2}{a-b}=\frac{3}{a+b}$

$\Rightarrow 2a+2b=3a-3b$

$\Rightarrow a=5b$

$\Rightarrow \frac{3}{a-b}=\frac{7}{3a+b-2}$

$\Rightarrow 9a+3b-6=7a+7b$

$\Rightarrow 2a-4b=6$

$\Rightarrow 2\left(5b\right)-4b=6(\because a=5b)$

$\Rightarrow 10b-4b=6$

$\Rightarrow 6b-6\Rightarrow b=1$ and $\Rightarrow a=5$