Question

The no of ordered pairs (x,y) satisfying 3x+2y=27 is a, then find the value of a,if x and y are non negetive integers

Answer 1

Given : The number of ordered pairs (x y).  satisfying 3x+2y = 27 is a,  x and

y are non-  negative integers ​

To find :   Value of a  

Solution:

3x  +   2y   =  27

=> 2y  =  27 - 3x

=> 2y = 3 ( 9 - x)  

=> y  = 3( 9 -  x) / 2

x & y are non negative integers

Hence 9 - x ≥ 0

=> x ≤ 9

also 9 - x must be Even  

Hence Possible Values of x  

are 9 , 7  ,  5   ,  3  ,   1

Corresponding y = 0  , 3  , 6 ,  9  ,  12

5 Ordered Pairs

= ( 9 , 0)  , ( 7 , 3) ,  (5 , 6)  , (3 , 9 ) , ( 1 , 12)

Hence  Value of  a = 5

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