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The number of integral values of m so that the abscissa of point of intersection of lines $3 x + 4 y = 9 and y = m x + 1$ is also an integer, is :

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answer is D.

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Detailed Solution

$\begin{array}{l} 3 x + 4 y = 9, y = m x + 1 \\ 3 x + 4 (m x + 1) = 9 \\ 3 x + 4 m x = 5 \\ x = \frac{5}{4 m + 3} ∣ \\ 4 m + 3 = \pm 1, \pm 5 \\ 4 m = - 2, - 4, 2, - 8 \end{array}$

$\begin{array}{l} m = - \frac{1}{2}, - 1, \frac{1}{2}, - 2 \\ m = - 1, - 2 \end{array}$

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