Question

$L_1:2x+y=50$ and $L_2:y=mx+1$ are two lines.

The greatest of integer values of $m$ for which the point of intersection of $L_1$ and $L_2$ has an integer as its $x-$coordinate is

• A. $5$
• B. $-9$
• C. $47$
• D. $-51$

Answer 1

The correct option is C $47$

The point of intersection of the given lines is $(\frac{49}{2+m},\frac{2+50m}{2+m})$.

For the x coordinate $\frac{49}{2+m}$ to be an integer 49 should be a multiple of $2+m.$

Hence $m$ can be $47,5,-1$ etc.

The largest value of $m$ is $47.$