Question

the number of integral solutions of 3x+3y+z=30

Answer 1

66 integral solutions of 3x+3y+z=30

Step-by-step explanation:

3x+3y+z=30

3(x + y) + z = 3 × 10

=> z = 3 (x + y - 10)

z must be a multiple of 3

z = 0 then x + y - 10 = 0

x can take 0 to 10 , 11 values

z = 3 , x + y - 10 = 1

x can take 0 to 9 , 10 values

z = 27, x + y - 10 = 9

x can take 0 to 1 , 2 values

z = 30 x + y - 10 = 10

x can take 0 , 1 values

11 + 10 + .........+ 2 + 1

= 11 * 12/2

= 66

66 solutions

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