Question:
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 :
Correct Option: , 2
Solution:
$3 x+4 y=9$
$y=m x+1$
$\Rightarrow 3 x+4 m x+4=9$
$\Rightarrow(3+4 \mathrm{~m}) \mathrm{x}=5$
$\Rightarrow \mathrm{x}$ will be an integer when
$3+4 m=5,-5,1,-1$
$\Rightarrow \mathrm{m}=\frac{1}{2},-2,-\frac{1}{2},-1$
so, number of integral values of $m$ is 2
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