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 + I is also an integer, is

The x-coordinate of the point of intersection is 3x + 4 (mx+1) - 9  or (3+4m)x=5 or x=53+4mFor x to be an integet,3 + 4m should be a divisor of 5, i.e., of 1, -1, 5, or -5. Hence, 3+4m=1 or m=−12 (not integer) 3+4m=−1 or m=−1 (integer) 3+4m=5 or m=12 (not an integer) 3+4m=−5 or m=−2 (integer) Hence, there are two integral values of m.