Question

Find the ordered pair (m,n), where m,n are positive integers satisfying the following equation:

Answer 1

Answer:
a valid solution is (1,3)

Explanation:
First, let' simplify the given equation:
14mn = 55 - 7m - 2n
14mn + 2n = 55 - 7m - 2n + 2n
n (14m + 2) = 55 - 7m
n = $\frac{55-7m}{14m+2}$

Now, we have only one equation in two unknowns. Therefore, the only way to solve this is by assuming one of the variables and solving for the other taking into consideration that both should be positive integers.

1- Assume m = 2:
n = $\frac{55-7(2)}{14(2)+2} = \frac{41}{30}$ .....> n is not a positive integer .........> This assumption is rejected

2- Assume m = 1:
n = $\frac{55-7(1)}{14(1)+2} = 3$ .......> both m and n are positive integers ........> This assumption is accepted ...........> Therefore, the solution would be (1,3)

Hope this helps :)