Question

The number of integral values of $m$ so that the abscissa of point of intersection of lines $3x+4y=9$ and $y=mx+1$ is also an integer, is:

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is B

$2$

Explanation for correct option:

Given equation of the lines are $3x+4y=9$ and $y=mx+1$

$$\begin{gathered} \therefore 3x+4y=9 \\ \Rightarrow 3x+4\left(mx+1\right)=9 \\ \Rightarrow x\left(3+4m\right)=9-4 \\ \Rightarrow x=\frac{5}{3+4m} \end{gathered}$$

Clearly $x$ will attain integer values when $3+4m=5,-5,1,-1$

$$\begin{gathered} 4m=5-3 \\ \Rightarrow m=\frac{1}{2} \end{gathered}$$,$$\begin{gathered} 4m=-5-3 \\ \Rightarrow m=-2 \end{gathered}$$,$$\begin{gathered} 4m=1-3 \\ \Rightarrow m=\frac{-1}{2} \end{gathered}$$,$$\begin{gathered} 4m=-1-3 \\ \Rightarrow m=-1 \end{gathered}$$

$\Rightarrow m=\frac{1}{2},-2,-\frac{1}{2},-1$

So number of integer values of $m$ is $2$

Hence option(B) is correct.