IIT-JEE 2001 ScreeningQuestion 1
The number of integer 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
Points and Straight Lines
Solution
Substituting $y=mx+1$: $x=\frac{5}{3+4m}$. Need $3+4m\in\{\pm1,\pm5\}$; with $m$ integer only $3+4m=-1,-5$, i.e. $m=-1,-2$. So $2$ values.