For what value of m, the system of equations $m x + 3 y = m - 3, 12 x + m y = m$ will have no solution.

-4

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-6

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Solution

The correct option is C
-6

Condition for any equations to have no solutions is,

$\frac{a_{1}}{a_{2}}$ = $\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

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

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

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

$\Rightarrow 3 m \neq m^{2} - 3 m$

$\Rightarrow 6 m \neq m^{2} \Rightarrow m \neq 6$

$∴ m = - 6$

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Similar questions

For what value of m, the system of equations $m x + 3 y = m - 3, 12 x + m y = m$ will have no solution.

Find the value of k for which each of the following systems of equations has no solution:

$k x + 3 y = 3, 12 x + k y = 6.$

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k x - 9 y = 66

2 x - 3 y = 8

3 x + m y = m

2 x - 5 y = 20

x > 0, y > 0

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