Question

The system of linear equations 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 what?
a)9
b)5
c)6
d)10

Answer 1

Answer-

the minimum possible value of (m+n) is equal to

Solution-

The system of linear equations  a₁x+b₁y=c₁ and a₂x+b₂=c₂ have infinitely many solutions when they coincide with each other. This will happen when,

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

Putting the values,

$\frac{5}{4}=\frac{m}{n}= \frac{10}{8}$

so if m is 5 parts, n must be 4 parts.

Therefore, the sum of a and b must be a multiple of and its minimum value will be 9