System of nonlinear equations

Definition

A system of nonlinear equations consists of two or more equations with at least one equation that is not linear, i.e., it involves variables raised to a power other than one or products of variables.

5 Must Know Facts For Your Next Test

1. Solutions to a system of nonlinear equations can be found graphically, algebraically, or numerically.
2. The solutions are the intersection points of the graphs of the equations involved.
3. Nonlinear systems can have no solution, exactly one solution, or multiple solutions.
4. Common methods to solve these systems include substitution and elimination.
5. Graphing calculators and computer software are often used to visualize and solve these systems.

Review Questions

• What distinguishes a nonlinear system from a linear system?
• Describe a method you can use to solve a system of nonlinear equations algebraically.
• $$\text{How many solutions can a system of nonlinear equations have?}$$

Related terms

Substitution Method: A technique for solving systems of equations by solving one equation for one variable and then substituting this expression into the other equation.

Elimination Method: A technique for solving systems of equations by adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variables.

$$Quadratic Equation$$: $$\text{An equation that can be written in the form } ax^2 + bx + c = 0 \text{ where } a \neq 0.$$