Question

For which values of ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ does the following pair of linear equations an 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

The correct option is A $a=5,b=1$

For infinite solutions
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\Rightarrow \frac{2}{a-b}=\frac{3}{a+b}=\frac{7}{3a+b-2}$
$\Rightarrow \frac{2}{a-b}=\frac{3}{a+b}\Rightarrow 2a+2b=3a-3b\Rightarrow a=5b$
$\Rightarrow \frac{3}{a+b}=\frac{7}{3a+b-2}\Rightarrow 9a+3b-6=7a+7b$
$\Rightarrow 2a-4b=6\Rightarrow 2\left(5b\right)-4b[\because a=5b]$
$\Rightarrow 10b-4b=6\Rightarrow 6b=6$
$\Rightarrow b=1,a=5$
Hence, option 'A' is correct.