Question

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

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is B $2$

$3x+4(mx+1)=9$
$\Rightarrow x(3+4m)=5$
$\Rightarrow x=\frac{5}{3+4m}$
$\Rightarrow (3+4m)=\pm 1,\pm 5$
$\Rightarrow 4m=-3\pm 1,-3\pm 5$
$\Rightarrow 4m=-4,-2,-8,2$
$\Rightarrow m=-1,-\frac{1}{2},-2,\frac{1}{2}$
Two integral value of $m.$