Question

Find the values of m and n for which the following system of linear equations has infinitely many solutions
$3x+4y=12(m+n)x+2(m-n)y=(5m-1)$

• A.
  4 and 1
• B.
  5 and 1
• C.
  5 and 2
• D.
  6 and 3

Answer 1

The correct option is B

5 and 1
If two linear equation has infinity many solutions means

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Here two linear equations are

$3x+4y=12and(m+n)x+2(m-n)y=5m-1i.e.:\frac{3}{m+n}=\frac{4}{2(m-n)}=\frac{12}{5m-1}6(m-n)=4(m+n)6m-6n=4m+4n2m-10n=\mathrm{0...}\left(1\right)\frac{3}{m+n}=\frac{12}{5m-1}3(5m-1)=12m+12n3m-12n=\mathrm{3.....}\left(2\right)Similarly\left(1\right)\times 3and\left(2\right)\times 26m-30n=06m-24n=6-------6n=6\Rightarrow n=1Nowfrom\left(1\right)2m-10=0m=5$