System of nonlinear equations

Definition

A system of nonlinear equations consists of two or more equations involving at least one variable raised to a power other than one or involving a product of variables. These systems can be solved using methods such as substitution, elimination, or graphical analysis.

5 Must Know Facts For Your Next Test

1. Nonlinear systems often involve quadratic, cubic, or higher-degree polynomial equations.
2. Graphical solutions may intersect at multiple points, and each intersection represents a solution to the system.
3. Substitution and elimination are common algebraic methods used to solve these systems.
4. Nonlinear systems can have no solution, exactly one solution, or multiple solutions.
5. The Jacobian matrix is sometimes used for solving nonlinear systems numerically.

Review Questions

• What are the common methods used to solve a system of nonlinear equations?
• How can you identify if a given system is nonlinear?
• What does each intersection point represent when solving a system of nonlinear equations graphically?

Related terms

Quadratic Equation: An equation where the highest exponent of the variable is squared (degree two).

Jacobian Matrix: A matrix representing all first-order partial derivatives of a vector-valued function.

Elimination Method: A method for solving systems of equations by adding or subtracting equations to eliminate one variable.