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

we know, if two linear equations are a₁x + b₁y + c₁ = 0 and a₂x + b₂y +c₂ = 0

a₁/a₂ = b₁/b₂ = c₁/c₂

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