# AII.5 and *AII.4 - Solving Non-Linear Systems

AII.5    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.

Bloom's Level:  Apply

### 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

• 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.

·  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

Systems of Linear

All.51  Predict the numbers of solutions to a nonlinear system  of two equations.

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

All.52  Solve a linear-quadratic system of two equations algebraically and graphically.

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