In mathematics, a trivial solution is a solution that is "obvious" or "simple". For example, the equation $x+5y=0$ has the trivial solution $x=0$ and $y=0$ . In contrast, a non-trivial solution is a solution that is not obvious or simple. In linear algebra, a trivial solution is a solution that has values of 0 for all variables in a system. Any solution in which at least one variable has a non-zero value is called a non-trivial solution. The term "trivial" is often used to refer to objects with a very simple structure, such as the empty set or a mathematical group containing only the identity element. The opposite of trivial is nontrivial, which is commonly used to indicate that an example or a solution is not simple or easy to prove.