Question

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

• A. 2
• B. 0
• C. 4
• D. 11

Answer 1

The correct option is A 2

Solving $3x+4y=9$ and $y=mx+1$, we get,

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

Since x is an integer, so $4m+3$ can take either of the values $1$ or $-1$ or $5$ or $-5$.

$4m+3=1⟹m=-\frac{1}{2}$

$4m+3=-1⟹m=-1$

$4m+3=5⟹m=\frac{1}{2}$

$4m+3=-5⟹m=-2$

Thus, the number of integral values of m is $2$.