Question

Find the values of m for which the pair of linear equations $2x+37-7=0$ and $(m-1)x+(m+1)y=(3m-1)$ has infinitely many solutions.

Answer 1

For infinitely many solutions,

$2x+37-7=0$

$\Rightarrow 2x+30$ ………$\left(1\right)$

$(m-1)x+(m+1)y-(3m-1)=0$ ………..$\left(2\right)$

Condition is,

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

$\frac{2}{m-1}=\frac{0}{m+1}=\frac{-30}{(3m-1)}$

$\frac{2}{m-1}=\frac{-30}{3m-1}$

$\Rightarrow 6m-2=-30m+30$

$\Rightarrow 36m=32$

$m=\frac{8}{9}$.