Question

The number of integer values of $m,$ for which $x$ 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 $2$

Point of intersection of $3x+4y=9$ and $y=mx+1$ is

$x=\frac{5}{3+4m}$ & $y=\frac{9m+3}{3+4m}$

So, value of $m$ such that $x$ co-ordinate is also integer

$m=0,x=\frac{5}{3}$

$m=-1,x=-5$

$m=-2,x=-1$

So, $m=-1$ & $-2$ this are two values of $m$ satisfy given condition.