This document discusses solving systems involving quadratic equations. It states that systems with one quadratic and one linear equation can have two solutions, one solution, or no solution. It outlines two methods for solving such systems: graphing the equations, and substituting one equation into the other. Students will learn to solve and graph both systems of linear and quadratic equations as well as systems of quadratic inequalities.

1. 4-9 THE QUADRATIC SYSTEMS
Chapter 4 Quadratic Functions and Equations
©Tentinger

2. ESSENTIAL UNDERSTANDING AND
OBJECTIVES
 Essential Understanding: you can solve systems
involving quadratic equations using methods similar
to the ones used to solve systems of linear equations
 Objectives:
 Students will be able to:
 Solve and graph systems of linear and quadratic
equations
 Solve and graph systems of quadratic inequalities

3. IOWA CORE CURRICULUM
 Algebra
 A.CED.3. Represent constraints by equations or
inequalities, and by systems of equations and/or
inequalities and interpret solutions as viable or non-
viable options in a modeling context
 A.REI.7* Solve a simple system consisting of a
linear equation and quadratic equation in two
variables algebraically and graphically

4. LINEAR-QUADRATIC SYSTEM
 Solutions of Linear Quadratic System
 A system of one quadratic equation and one linear
equation can have two solutions, one solution, or
no solution.
 NEED PICTURES OF EACH

5. SOLVING A LINEAR-QUADRATIC SYSTEM BY
GRAPHING

6. SOLVING A LINEAR-QUADRATIC SYSTEM BY
SUBSTITUTION

7. SOLVING A QUADRATIC SYSTEM OF
EQUATIONS BY SUBSTITUTION

8. SOLVING A QUADRATIC SYSTEM OF
INEQUALITIES

9. HOMEWORK
 Pg. 262 – 263
 #9 – 51 (3s), 53 - 55