Chapter 6
Systems of Equations and Inequalities
Objectives for this Chapter:
-Identify solutions of systems of linear equations in two variables
-Solve systems of linear equations in two variables by graphing
-Solve systems of linear equations in two variables by substitution
-Solve systems of linear equations in two variables by elimination
-Write a system of equations from a word problem and then solve
the system of equations to answer the question
-Solve special systems of linear equations in two variables
-Classify systems of linear equations and determine the number of
solutions
-Graph and solve linear inequalities in two variables
-Graph and solve systems of linear inequalities in two variables
-Write a system of inequalities from a word problem and then graph
the system to answer the question.
6.4
Solving Special Systems
Solve each system of equations
using substitution or elimination.
{
y = -4x + 1
4x = -y - 6
{
y-x+3 = 0
x = y+3
A consistent system is a system with
at least one solution.
An inconsistent system is a system
with no solutions.
An independent system has
exactly one solution.
A dependent system has
infinitely many solutions.
consistent and
independent
consistent and
dependent
inconsistent
exactly one
solution
infinitely many
solutions
no
solutions