SOLUTION: How many points in the first quadrant satisfy both of the following conditions: (i) the x and y coordinates are positive integers and (ii) x + y ≤ 5?

Question 203188: How many points in the first quadrant satisfy both of the
following conditions: (i) the x and y coordinates are positive
integers and (ii) x + y ≤ 5?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since "x" and "y" are both positive integers (ie positive whole numbers 1, 2, 3, 4, etc...) just ask yourself: "what two numbers add to another number that is either less than or equal to 5?"

So for instance, 2+2=4 which is less than or equal to 5. Also, 1+2=3 which is also less than or equal to 5. Furthermore, 2+3=5 which is less than or equal to 5.

These values can be thought of as the ordered pairs (2,2), (1,2), and (2,3)

Here are all of the possible ordered pairs

(0, 0),
(0, 1),
(0, 2),
(0, 3),
(0, 4),
(0, 5),
(1, 0),
(1, 1),
(1, 2),
(1, 3),
(1, 4),
(2, 0),
(2, 1),
(2, 2),
(2, 3),
(3, 0),
(3, 1),
(3, 2),
(4, 0),
(4, 1),
(5, 0)

So for example, the ordered pair (1,4) means that 1+4=5 which is less than or equal to 5.
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SOLUTION: How many points in the first quadrant satisfy both of the following conditions: (i) the x and y coordinates are positive integers and (ii) x + y &#8804; 5?

SOLUTION: How many points in the first quadrant satisfy both of the following conditions: (i) the x and y coordinates are positive integers and (ii) x + y ≤ 5?