SOLUTION: What are all ordered triples of numbers (x, y, z) which satisfy the system of equations (x + y)(z + 1) = 24, (x + y)(y + 1) = 24, and (y + z)(x + 1) = 24?

Question 574555: What are all ordered triples of numbers (x, y, z) which satisfy the system of equations
(x + y)(z + 1) = 24,
(x + y)(y + 1) = 24, and
(y + z)(x + 1) = 24?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

, and

Combining the first two equations

So cannot be zero and
If , the third equation turns into
---> --> --> which can be substituted into one of the other equations
--> --> --> --> -->
Substituting into we get
--> -->
That can be solve by factoring, starting by factoring out , because it's obvious that is a solution
--> -->
SO the solutions are
-->
-->
-->
The solutions would be (11,1,1), (3,3,3) and (-4,-4,-4).

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