Question

The number of integral values of $m,$ for which the $x-$coordinate of the point of intersection of the lines $3x+4y=9$ and $y=mx+1$ is also an integer is

• A. $2$
• B. $0$
• C. $4$
• D. $11$

Answer 1

The correct option is A $2$

$3x+4y=\mathrm{9.....}\left(i\right)$
$y=mx+\mathrm{1......}\left(ii\right)$
putting (ii) in (i) we get $3x+4mx=5⟹x=\frac{5}{3+4m}$
For $x$ to be integer $3+4m=\pm 5,\pm 1$ as the denominator must divide the numerator or must be equal to $\pm 1$ so to divide the numerator completely

$⟹m=-1,-2,\frac{1}{2},\frac{-1}{2}$
$m$ has two integral values.