1.5k views
0 votes
What is the number of ordered pairs (x,y) that are solutions to

4x+5y=2017
where both x and y are positive integers?

User Baddack
by
4.3k points

1 Answer

3 votes

Answer:

Explanation:

An ordered pair is a pair of coordinates on a graph that satisfy a particular equation.

From our question, the given equation is

4x + 5y = 2017

5y = 2017 - 4x

y = (2017 - 4x) / 5

but (x,y) are positive integers meaning that x and y > 0

when x = 1, y = (2017 - 4) /5

y = 2013/5

=402.6

Hence (x.y) = (1. 402.6) which is not a solution to the equation

when x = 2 , y = (2017 -8) /5

y = 2009/ 5 = 401.8

(x,y) = (2, 401.8) which is not a solution to the equation

when x = 3 , y = (2017 - 12)/ 5

y = 2005/5 = 401

(x, y) = (3, 401) which is a solution to the equation

when x =5 , y = (2017 - 20) / 5

y = 1997/5 = 399.4

(x,y) = (5, 399.4) which is not a solution to the equation

User Robert Wagstaff
by
4.0k points