Question

If the point of intersection of the lines $3x+4y=9$ and $y=mx+1$ is integer (both $x$ and $y$ co-ordinates are integer) , then sum of all possible values of $m$ is

• A. $-1$
• B. $-2$
• C. $-3$
• D. $-4$

Answer 1

Answer: (C)

$-3$

Given lines

$3x+4y=9$------(1)

$y=mx+1$------(2)

putting eq (2) in (1)

$3x+4(mx+1)=9$

$\Rightarrow 3x+4mx+4=9$

$\Rightarrow (3+4m)x=5$

$\Rightarrow x=\frac{5}{3+4m}$

now from eq (2)

$y=m\left(\frac{5}{3+4m}\right)+1$

$y=\frac{9m+3}{4m+3}$

Now, clearly possible values of m are -2,-1 to ve integer

Hence sum$=-3$