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=m x+1` is also an integer is (a) 2 (b) 0 (c) 4 (d) 1

Options

A. 2
B. 0
C. 4
D. 1

Answer

A

Explanation

The coordinates of the point of intersection of the given lies are
`((5)/(3+4m),(3+9m)/(3+4m))`
It is given that the x -coordinate of this point is an interger.
`therefore (5)/(3+4m)` is an integer
`rArr 3 + 4m` is a divisor of 5
`rArr 3 + 4 m = 1, 3+ 4m =-1, 3+ 4m = 5, 3+4m =-5`
`rArr m = - 1,2 [{:(because "3 + 4m =1,3+4m= 5 do not"),("give intergal value of m"):}]`
Hence, there are two value of m.