Question

The cardinal number of the integral solution set formed by the inequations x > 0, 7x + 4y 0 is?? Please explain

Answer 1

Answer:

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) }