Suppose x and y are natural numbers, then the number
of ordered pairs (x,y) which satisfy
[tex]x + y \leqslant 5[/

2 thoughts on “Suppose x and y are natural numbers, then the number<br />of ordered pairs (x,y) which satisfy <br />[tex]x + y \leqslant 5[/”

1. Answer:

   4

   Step-by-step explanation:

   As x and y are natural numbers, the cannot be 0

   so the possible pairs are

   (4,1)

   (1,4)

   (2,3)

   (3,2)

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2. Given :– x + y ≤ 5 . also x and y are natural numbers .

   Answer :–

   taking x = 1 , Possible values of y,

   • y = 1 => x + y = 1 + 1 = 2 < 5 . { since it is not given x ≠ y}
   • y = 2 , => 1 + 2 < 5 .
   • y = 3 => 1 + 3 < 5
   • y = 4 => 1 + 4 ≤ 5

   So, at x = 1 we gets 4 pairs .

   now, at x = 2 ,

   • y = 1 , => 2 + 1 < 5
   • y = 2 , => 2 + 2 < 5
   • y = 3 , => 2 + 3 ≤ 5 .

   So, at x = 2 we gets 3 pairs .

   similarly, at x = 3 ,

   • y = 1, => 3 + 1 < 5
   • y = 2, => 3 + 2 ≤ 5 .

   So, at x = 3 we gets 2 pairs .

   now, at x = 4,

   • y = 1 => 4 + 1 ≤ 5 .

   So, at x = 4 we gets 1 pairs .

   then,

   → Total order of pairs = 4 + 3 + 2 + 1 = 10 (Ans.)

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