Question

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

• A. $2$
• B. $0$
• C. $4$
• D. $1$

Answer 1

The correct option is A $2$

Given lines $3x+4y=9$ and $y=mx+1$
Finding the $x-$ coordinate of point of intersection, we get
$3x+4(mx+1)=9\Rightarrow x=\frac{5}{4m+3}$

$\therefore \frac{5}{3+4m}$ is an integer
$\Rightarrow 3+4m$ is a divisor of $5$
$3+4m=1,3+4m=-1,3+4m=5,3+4m=-5$
$m=-\frac{1}{2},-1,\frac{1}{2},-2\therefore m=-2,-1$

Hence, there are two values of $m$.