Question

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

Answer 1

Answer:
A valid solution would be (1,3)

Explanation:
First, we will try to simplify the given equation as follows:
14mn = 55 - 7m - 2n
14mn + 2n = 55 - 7m - 2n + 2n
n (14m + 2) = 55 - 7m
n = $\frac{55-7m}{14m+2}$

Now, we are given only one equation with two unknowns. Therefore, to solve this equation, we will need to assume the value of one of the variables and solve for the other. Then we will check if the solution matched the given condition (that the two numbers are positive integers or not).

1- Assume that m = 3:
n = $\frac{55-7(3)}{14(3)+2}$ = 17/22 .....> n is not a positive integer......> this solution is rejected

2- Assume m = 2:
n = $\frac{55-7(2)}{14(2)+2}$ = 41/30 .....> n is not a positive integer......> this solution is rejeceted

3- Assume m = 1:
n = $\frac{55-7(1)}{14(1)+2}$ = 3 ........> both m and n are positive integers .......> this solution is accepted

Based on the above, a valid solution would be (1,3)

Hope this helps :)