Question

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+1 is also an integer is (a) 2 (b) 0 (c)4 (d)1

Answer 1

Coordinates of the point of intersection of the lines y = mx + 1 ------ (1)
and 3x + 4y = 9 ------------ (2) is the solution set of the equations.

Substituting the value of y in equation (2),
3x + 4(mx + 1) = 9
3x + 4mx + 4 = 9
x(4m + 3) = 5
x = 5 / (4m + 3)

Case (i)

If 4m + 3 = 5

⇒ 4m = 2

⇒ m = 1/2

Case (ii)

If 4m + 3 = - 5

⇒ 4m = - 8

⇒ m = - 2

Case (iii)

If 4m + 3 = 2

⇒ 4m = -1

⇒ m = -1/4

Therefore, integral value of m is -2 for which the x-coordinate of the point of intersection of lines is an integer.