AII.5 
The student will solve nonlinear systems of equations, including linearquadratic and quadraticquadratic, algebraically and graphically. Graphing calculators will be used as a tool to visualize graphs and predict the number of solutions. 

Essential Knowledge and Skills 
 Predict the number of solutions to a nonlinear system of two equations.
 Solve a linearquadratic system of two equations algebraically and graphically.
 Solve a quadraticquadratic system of two equations algebraically and graphically.

Essential Understandings 
 Solutions of a nonlinear system of equations are numerical values that satisfy every equation in the system.
 The coordinates of points of intersection in any system of equations are solutions to the system.
 Realworld problems can be interpreted, represented, and solved using systems of equations.


Vertical Articulation 
 SOL A.4  e) solve systems of two linear equation (2 variable‐ algebraically/graphically);
 SOL A.5  d) solve systems of inequalities.
 SOL AFDA.5  determine opt values in problem situations by identifying constraints/using linear programming techniques

Instructional Materials 
 VDOE ESS Lesson: Nonlinear Systems of Equations  Equations and Inequalities (PDF)  Solving nonlinear systems of equations (Word)
 Notes: Solving Systems Algebraically (ppt)
 Notes: Points of Intersection (flipchart)
 Notes: Solving Systems with CASIO (doc)
 Notes: Solving Systems with TI84 (doc)

Real World Lessons 

Practice 
 VDOE ESS: LinearQuadratic System Practice Worksheet (pdf)
 VDOE ESS: QuadraticQuadratic System Exploration Worksheet (pdf)
 VDOE ESS: QuadraticQuadratic System Practice Worksheet (pdf)
 Worksheet: Solving Systems Practice (doc)

SelfAssessments 
 SOL MiniQuiz: AII.5  Solving Systems of Quadratic and Linear Equations Algebraically

Skills 
 JMU Pivotal Question: Systems of Nonlinear Equations (doc)

Videos 

Explore
Learning 
 Modeling Linear Systems  Activity A  Experiment with a system of two lines representing a cat‑and‑mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real‑world meaning to slope, y‑intercept, and the intersection of lines.
 Solving Linear Systems by Graphing  Compare a system of equations in standard form or in slope‑intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
 Special Types of Solutions to Linear Systems  Compare a system of equations in standard form to its graph. Examine the graph and table of values. Determine the solutions to the system.
 Systems of Linear Equations  Activity A  Solve a system of linear equations by graphing and finding the intersection of the lines of the equations. Create a system of equations, examine its graph, matrix, and table of values, and determine the solution of the system.

Websites 
 LinearQuadratic Systems  Solving a LinearQuadratic System Graphically from Regentsprep.com

Common Core
Standards 
