Question

The number of integer 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.
• B.
• C.
• D.

Answer 1

The correct option is A

$3x+4(mx+1)=9$
$\Rightarrow x=\frac{5}{3+4m}$ ....(i)
Since, x is an integer, then by equation (i), we have
$3+4m=-1,1,5,-5$
$\Rightarrow m=-1,-\frac{1}{2},\frac{1}{2},-2$
$\therefore m=-1,-2ϵ1$
Thus, the number of integer values of m is 2.