Question

For which value of m, the pair of linear equations $8x+my=m–4$ and $(m–1)x+7y=m$ does not have a unique solution?

• A. 5
• B. -10
• C. -7
• D. 9

Answer 1

The correct option is C -7

The pair of linear equations $8x+my=m-4$ and $(m-1)x+7y=m$ has no unique solution. For inconsistance solution, $\frac{a_1}{a_2}=\frac{b_1}{b_2}$
$\Rightarrow \frac{8}{m-1}=\frac{m}{7}$
$\Rightarrow m^2-m=56$
$\Rightarrow m^2-8m+7m-56=0$
$\Rightarrow m(m-8)+7(m-8)=0$
$\Rightarrow (m-8)(m+7)=0$
$\Rightarrow m=8\text{or}m=-7$
Hence the correct answer is Option (3)