College Algebra Chapter 5 Systems of Equations and Inequalities Section 5.4 Systems of Nonlinear Equations in Two Variables Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Concepts Solve Nonlinear Systems of Equations by the Substitution Method Solve Nonlinear Systems of Equations by the Addition Method Use Nonlinear Systems of Equations to Solve Applications

Concept 1 Solve Nonlinear Systems of Equations by the Substitution Method

Example 1 Solve by substitution:

Example 2 Solve by substitution:

Skill Practice 1 Solve by system by using the substitution method.

Skill Practice 2 Solve by system by using the substitution method.

Concept 2 Solve Nonlinear Systems of Equations by the Addition Method

Example 3 Solve by addition:

Example 4 Solve by addition:

Example 5 Solve by addition:

Skill Practice 3 Solve by system by using the addition method.

Skill Practice 4 Solve by system by using the addition method.

Concept 3 Use Nonlinear Systems of Equations to Solve Applications

Example 6 A right triangle has a hypotenuse measuring 13 inches and an area of 30 square inches. Find the length of each leg.

Skill Practice 5 The perimeter of a rectangular rug is 40 feet and the area is Find the dimensions of the rug.