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) 2

(b) 0

(c) 4

(d) 1

Answer 1

Correct option is (a) 2

Point of intersection \(\left(\frac5{3 +4m}, \frac{3+9m}{3+4m}\right)\)

x-coordinate is an integer when 3 + 4m = ±1 or ±5.

\(m = -1, -2, -\frac12 , \frac 12\)

Hence there are two values of m.