Question

the system of linear equation 5x+my=10 and 4x+ny=8 have infinitely many solutions where m and n are positive integers.then the minimum possible value of (m+n) is equal to

Answer 1

nice question of God will bless you

Answer 2

we know, if two linear equations are $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$

for infinity many solutions :
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

here two linear equations are :
5x + my = 10 => 5x + my - 10 = 0
4x + ny = 8 => 4x + ny - 8 = 0

for infinity many solutions , 5/4 = m/n = -10/-8
or, 5/4 = m/n = 5/4
so, least value of m is 5 and n is 4.

hence, minimum possible value of (m + n) =9