Algebra 2 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities



SOL Review Materials
The student will solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, 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 linear-quadratic system of two equations algebraically and graphically.
  • Solve a quadratic-quadratic 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.
  • Real-world problems can be interpreted, represented, and solved using systems of equations.
Vertical Articulation
  1. SOL A.4 - e) solve systems of two linear equation (2 variable‐ algebraically/graphically);
  2. SOL A.5 - d) solve systems of inequalities.
  3. SOL AFDA.5 - determine opt values in problem situations by identifying constraints/using linear programming techniques
Instructional Materials
  1. VDOE ESS Lesson: Nonlinear Systems of Equations - Equations and Inequalities (PDF) - Solving nonlinear systems of equations (Word)
  2. Notes: Solving Systems by Graphing using CASIO (ppt)
  3. Notes: Solving Systems by Graphing using TI-84 (ppt)
  4. Notes: Solving Systems with CASIO (doc)
  5. Notes: Solving Systems with TI-84 (doc)
Real World Lessons
  1. VDOE ESS: Linear-Quadratic System Practice Worksheet (pdf)
  2. VDOE ESS: Quadratic-Quadratic System Exploration Worksheet (pdf)
  3. VDOE ESS: Quadratic-Quadratic System Practice Worksheet (pdf)
  4. Worksheet: Solving Systems Practice (doc)
  1. SOL Mini-Quiz: AII.5 - Solving Systems of Quadratic and Linear Equations Graphically
  1. JMU Pivotal Question: Systems of Nonlinear Equations (doc)
Explore Learning
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  1. Linear-Quadratic Systems - Solving a Linear-Quadratic System Graphically from
Common Core Standards