The number of integer value 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

x-coordinate of the point of intersection is given by3x+4(mx+1)=9⇒x=53+4mAs x is an integer, 3+4m must be a divisor of 5so, 3+4m=±1 or ±5⇒m=−1 or −2(considering the integer value only)