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 alsoan integer

Solving two equations 3x + 4y = 9 and y = mx + 1, we get x=53+4mNow x is integer if 3 + 4m = 1, -1, 5 or -5∴m=−12,−1,12,−2So, the integral values of m are -1 and -2 and clearly, for these values of m, x is integer