# AII.4 - Solving Non-Linear Systems

### BIG IDEAS

• I can create telescope and wide-angle camera lenses, reconstruct traffic accidents for investigation, monitor aircraft flight patterns as an air traffic controller, analyze crimes for police officers, and work as a seismologist or geologist.
• I will be able to solve systems involving linear and quadratic equations, by quadratic equations only by graphing, algebraically, and by using a calculator to visualize the solution.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - AII.4 Understanding

·  Quadratic equations included in this standard will only include those that can be represented as parabolas of the form  where .

·  Solutions of a system of equations are numerical values that satisfy every equation in the system.

·  A linear-quadratic system of equations may have zero, one, or two solutions.

·  A quadratic-quadratic system of equations may have zero, one, two, or an infinite number of solutions.

·  The coordinates of points of intersection in any system of equations are solutions to the system.

·  Practical problems can be interpreted, represented, and solved using systems of equations.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  AII.41  Determine the number of solutions to a linear-quadratic and quadratic-quadratic system of equations in two variables.

·  AII.42  Solve a linear-quadratic system of two equations in two variables algebraically and graphically.

·  AII.43  Solve a quadratic-quadratic system of two equations in two variables algebraically and graphically.

·  AII.44  Solve systems of equations and verify solutions of systems of equations with a graphing utility.

### KEY VOCABULARY

nonlinear, linear, quadratic, algebraically, graphically, predict

Updated: Aug 23, 2018