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. $1$

Answer 1

The correct option is A $2$

By solving both equations for x coordinate, we get

$mx+1=\frac{9-3x}{4}$

$\Rightarrow 4mx+4=9-3x$
Or, $3x+4mx+4=9$
Or, $x=5/(3+4m)$

Since x has to be an integer, possible values of x are $5,-5,1,-1$ for which,

the denominator on R.H.S. has to be $1,-1,5,-5$ respectively.

Now, $3+4m=1$,implies $m=-0.5$
$3+4m=-1$, implies $m=-1$
$3+4m=5$, implies $m=0.5$

$3+4m=-5$, implies $m=-2.$

Hence, two integral values of m are possible.