Question

Hello friends !

The number of non negative integral solution of the equation , X + y + 3z = 33 is

Answer 1

Let us look at the given constraints:

x, y, z are non-negative integers =>x>=0,y>=0,z>=0x>=0,y>=0,z>=0

x+y+3z=33=>y=33−3z−x—(1)x+y+3z=33=>y=33−3z−x—(1)

12 possible values for z are 0,1,2,3,4,5,6,7,8,9,10,110,1,2,3,4,5,6,7,8,9,10,11

If z=0, From (1), y = 33 - x => x can have values from 0, 1, .. 33 => 34 possibilities

If z=1, from (1), y = 33 - 3 - x = 30 - x => x can have 31 possibilities ( 0,1,2, .. 30)

If z=2, from (1), y = 33 - 6 - x = 27 - x => x can have 28 possibilities ( 0,1,2, .. 27) and so on

If z=11, from (1) y = 33 - 33 - x = -x => Only one possible combination with x = y = 0

Total possibilities =34+31+28+…+134+31+28+…+1

This is AP with a = 34, d = -3 and n=12

Total possibilities = 34+31+28+…+1=122∗[(2∗34)+(12–1)∗(−3)]=6∗[68−33]=210


PLZ mark me BRAINLIEST

Answer 2

HeY !!!

Here is ur solution !!
__________________

Consider case when z = 0, 1, 2, ..........11

=> x + y = 33, 30, 27 .......

= 34 + 31 + 28 +.........+ 1 ( 12 times )

12/2 ( 1 + 34) = 210 Answer ✔

________________________________

Hope it helps you !!!

@Rajukumar111