Solving Non-Linear Systems of Equations

In this section, we learn how to solve a system of non-linear equations. When we see an equation where some terms have more than one variable or a variable in which the exponent is 2 or larger, we refer to this equation as non-linear. When we encounter a non-linear system of equations, at least one of the equations is non-linear. To solve a non-linear system of equations, we rely on substitution, elimination, or a combination of the two methods. We will show how to solve a non-linear system that contains one linear equation and one second-degree equation using substitution. We will then move into using the elimination method to solve a non-linear system that involves 2 second-degree equations. Lastly, we will look at some non-linear systems that require a combination of the substitution and elimination methods.