How many solutions using nonnegative integers are there to the equation x + y + z = 10. list the different solutions.

65

Step-by-step explanation:

Since we have

x = -(y+z)+10

the solutions are the points (x,y,z) such that y,z non negative integers with y+z ≤ 10

There are 65 possible solutions.

The list of solutions is the following

x=10, y=z=0

x=9, y=0, z=1

x=8, y=0, z=2

x=7, y=0, z=3

x=6, y=0, z=4

x=5, y=0, z=5

x=4, y=0, z=6

x=3, y=0, z=7

x=2, y=0, z=8

x=9, y=0, z=1

x=9, y=1, z=0

x=8, y=1, z=1

x=7, y=1, z=2

x=6, y=1, z=3

x=5, y=1, z=4

x=4, y=1, z=5

x=3, y=1, z=6

x=2, y=1, z=7

x=1, y=1, z=8

x=0, y=1, z=9

x=8, y=2, z=0

x=7, y=2, z=1

x=6, y=2, z=2

x=5, y=2, z=3

x=4, y=2, z=4

x=3, y=2, z=5

x=2, y=2, z=6

x=1, y=2, z=7

x=0, y=2, z=8

x=7, y=3, z=0

x=6, y=3, z=1

x=5, y=3, z=2

x=4, y=3, z=3

x=3, y=3, z=4

x=2, y=3, z=5

x=1, y=3, z=6

x=0, y=3, z=7

x=6, y=4, z=0

x=5, y=4, z=1

x=4, y=4, z=2

x=3, y=4, z=3

x=2, y=4, z=4

x=1, y=4, z=5

x=0, y=4, z=6

x=5, y=5, z=0

x=4, y=5, z=1

x=3, y=5, z=2

x=2, y=5, z=3

x=1, y=5, z=4

x=0, y=5, z=5

x=4, y=6, z=0

x=3, y=6, z=1

x=2, y=6, z=2

x=1, y=6, z=3

x=0, y=6, z=4

x=3, y=7, z=0

x=2, y=7, z=1

x=1, y=7, z=2

x=0, y=7, z=3

x=2, y=8, z=0

x=1, y=8, z=1

x=0, y=8, z=2

x=1, y=9, z=0

x=0, y=9, z=1

x=0, y=10, z=0

d

step-by-step explanation: