# Solve returns empty list

I want to solve these equations but Mathematica gives no answer.

X :=
3/2 x (-((γ y (1 - z)^3 (-x^2 - y^2 + 1)^2)/z^3) + x^2 - y^2 - 1) -
(λ y z)/(1 - z);

Y :=
-((3 γ (y^2 - 1) (1 - z)^3 (-x^2 - y^2 + 1)^2)/(2 z^3)) + 3/2 y (x^2 - y^2 + 1) +
(λ x z)/(1 - z);

Z :=
3/2 ((1 - z) z (x^2 - y^2 + 1) - (γ y (1 - z)^4 (-x^2 - y^2 + 1)^2)/z^2);

Solve[X == Y == Z == 0, {x, y, z}]


{}

What do I do?

• Reduce[{X == Y == Z == 0}, {x, y, z}]
– user36273
Jun 25, 2016 at 10:25
• As a side note, it is considered bad form to use capital letters as declared variables. Or to use multi-letter variables that start with capital letters. Jun 25, 2016 at 11:41
• This system cannot be solved with the methods available to Solve. (or Reduce) Jun 26, 2016 at 3:03
• @Young Do you Know another method? Jun 26, 2016 at 7:32
• @milad , @Young This system can be solved with Reduce!
– user36273
Jun 26, 2016 at 12:35

Please check the documentation on Solve.
{} means that your system has no solutions in general.
Reduce does give a solution, but notice that it comes with the specific condition that λ == 0. For general λ there is no solution.
Solve gives generic solutions only. Another excerpt from the documentation:
Solve gives generic solutions only. Solutions that are valid only when continuous parameters satisfy equations are removed. Other solutions that are only conditionally valid are expressed as ConditionalExpression objects.