Let x, y, and z be real numbers such that
x + y - z = 8
x + y + z = 18
-x + 2y + z = 10.
Compute xyz.
From the first equation, we get:
-z + x = 8 - y
And the third equation gievs us:
z - x = 10 - 2y.
Since we know that -z + x is -1 times z - x, we know that:
8 - y = 2y - 10
This gives us: y = 6
Substiting this value into the first two equations gives us:
x = 7, z = 5
From here, we get 210 as our answer.
