The Sylvester Equation is a type of algebraic equation that helps us figure out how to solve problems involving different numbers and symbols. It works by using two mathematical expressions that have the same number of variables (symbols). We then use these expressions to help us come up with the right answer to a problem. For example, if we have the equation 3 + x = 15, we can use the Sylvester Equation to work out that the answer to the problem is x=12.