The number of integer oalues of m, for which the x-coordinaie of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer

The coordinates of the point of intersection of the given lines are53+4m−3+9m3+4mIt is given that the x-coordinate of this point is an integer∴ 53+4m is an integer ⇒ 3+4m is a divisor of 5⇒ 3+4m=1,3+4m=−1,3+4m=5,3+4m=−5⇒ m=−1,−2 ∵3+4m=1,3+4m=5 do not  give integral values of mHence, there are two values of m.