Question

If $3x+y=11$ and $(m+n)x+(m–n)y=5m+n$ has infinitely many solutions, then the value of m and n respectively can be

• A. 6,4
• B. 5,1
• C. 6,3
• D. 3,6

Answer 1

The correct option is C 6,3

Given that $3x+y=11$ and $(m+n)x+(m–n)y=5m+n$ has infinitely many solutions
For pair of lines $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ to have infinitey many solutions, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\therefore$ For infinity solution of $3x+y=11$ and $(m+n)x+(m-n)y=5m+n,$
$\frac{3}{m+n}=\frac{1}{m-n}=\frac{11}{5m+n}$
$\Rightarrow 3m-3n=m+n\text{and}5m+n=11m-11n$
$\Rightarrow 2m=4n\text{and}12n=6m$
$\Rightarrow m=2n$

So, m should be twice of n.
Thus, 6 and 3 can be the possible values of m and n, respectively.
Hence, the correct answer is option (3).