Question

The cardinal number of the integral solution set formed by the inequations x > 0,
7x + 4y < 28 and y > 0 is????​

Answer 1

Given :  7x + 4y < 28  ,  x > 0  y > 0

To find : The cardinal number of the integral solution set formed

Solution:

x  >  0

y  > 0

7x + 4y < 28

x = 1

=> 7 + 4y < 28

=>  4y < 21

=> y ≤ 5

=> y  = 1  , 2 , 3 , 4 , 5

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

x = 2

=> 14 + 4y < 28

=>   4y < 14

=> y ≤ 3

=> y  = 1  , 2 , 3

(2 , 1) , ( 2 2) , (2, 3)  

x = 3

=> 21 + 4y < 28

=>   4y < 7

=> y ≤ 1

=> y  = 1  

(3 , 1)  

x = 4

28 + 4y < 28

=> y < 0  ( not possible)

The cardinal number of the integral solution set  

{(1 , 1) , ( 1, 2) , (1 , 3) , ( 1, 4) , ( 1, 5) , (2 , 1) , ( 2 2) , (2, 3)  , (3 , 1)   }

9 Solutions

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