Answer:
65
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