Question

The number of integral values of m, for which the 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. 4
• C. 1

Answer 1

The correct option is A 2

Solving given lines for the x-coordinate of the point of intersection
3x+4(mx+1)= 9
or $(3+4m)x=5orx=\frac{5}{3+4m}$
For x to be an integer, 3+4m should be a divisor of 5, i.e., $1,-1,5,or-5.$ Hence,
$3+4m=1orm=-\frac{1}{2}\left(notaninteger\right)3+4m=-1orm=-1\left(integer\right)3+4m=5orm=\frac{1}{2}\left(notaninteger\right)3+4m=-5orm=-2\left(integer\right)$
Hence, there are two integral values of m.