Question

The number of integer values of m, for which the x co-ordinate of the point of intersection of the lines $3x+4y=0$ and $y=mx+1$ is also an integer, is

• A. $2$
• B. $0,-1$
• C. $4$
• D. $1$

Answer 1

Answer: (B)

$0,-1$

Solve both eqns simply and take out (x,y) coordinates.
put y = mx +1 in 3x + 4y – 9 = 0
U would get,
3x + 4(mx + 1) – 9 = 0
(3 + 4m)x = 6 
x = > 6/(3 + 4m)
and y = 6m/(3+4m) + 1 = > (7m +3)/(3+4m)
Now for x to be integer,
the modulus of denominator value should not be greater equals than 6.
Therefore,
(3+4m) less than equal to 6 and greater than -6
on solving m would satify as
m = 0, -1 .