#### Math - 2019-20

# AII.4 - Solving Non-Linear Systems

AII.4The student willsolvesystems of linear-quadratic and quadratic-quadratic equations, algebraically and graphically.

*Adopted: 2016*

### 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

· 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.4_{1} **Determine**
the number of solutions to a linear-quadratic and quadratic-quadratic system of
equations in two variables.

·
AII.4_{2} **Solve**
a linear-quadratic system of two equations in two variables algebraically and
graphically.

·
AII.4_{3} **Solve**
a quadratic-quadratic system of two equations in two variables algebraically
and graphically.

·
AII.4_{4} **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*