Objectives
 Define nonlinear system of equations.
 Determine the number of solutions that a system of nonlinear equations has when given a graph of the system.
 List the steps for solving systems of nonlinear equations using the substitution method.
 Solve systems of nonlinear equations.
 Use algebra to isolate a variable in a nonlinear equation.
Key Terms
 Quadratic Formula – A formula used to solve quadratic equations.
 The solutions to the quadratic equation are given by the formula .
 Isolate – To separate from others.
 To get the variable alone on one side of the equation or inequality.
 Nonlinear System of Equations – A group of nonlinear equations that have the same variables and are used together to solve a problem.
 The equations may be some combination of linear equations and nonlinear equations (all may be nonlinear, or only one may be nonlinear).
 System of Linear Equations – A group of linear equations that have the same variables and are used together to solve a problem.
 A linear equation can be written in the form y = mx + b.
 The graph of a linear equation is a straight line.
Notes
Solutions of Nonlinear Systems of Equations 


Step 1: Isolate y in the 1st equation (divide by 3 on both sides). Step 2: Substitute the yvalue of “4x” into the 2nd equation. Step 3: Square the 4x term. 
Answer: 4 Look for where the ellipse and hyperbola intersect. 
