Extraneous solutions are solutions to an equation or system of equations that satisfy the equation(s) but do not represent valid solutions to the problem being modeled. They can arise from a variety of sources, including: Incorrect algebraic manipulations Assuming that a particular solution exists when it does not Failing to consider the domain of the variables involved It is important to check for extraneous solutions whenever solving an equation or system of equations, as they can lead to incorrect conclusions.
There are a number of methods that can be used to check for extraneous solutions, including: Substituting the solution back into the original equation(s) to see if it satisfies them Checking to see if the solution makes sense in the context of the problem being modeled Using a graphing calculator or computer program to plot the graph of the equation(s) and see if the solution is on the graph By following these steps, you can help ensure that the solutions you obtain to equations and systems of equations are valid solutions to the problems you are trying to solve.
