Question

For what value of m, the system of equations $mx+3y=m–3,and12x+my=m$ will have no solution.

• A. -4
• B. 4
• C. -6
• D. 6

Answer 1

The correct option is C

-6

Condition for any pair of equations to have no solutions is,

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

$\frac{m}{12}$= $\frac{3}{m}$

$\Rightarrow m^2=36\Rightarrow m=6,-6$

$\frac{3}{m}\ne \frac{m-3}{m}$

$\Rightarrow 3m\ne m^2-3m$

$\Rightarrow 6m\ne m^2\Rightarrow m\ne 6$

$\therefore m=-6$