Chapter 4:Systems of Linear

Equations and Inequalities

Section 4-1:Introduction to Linear Systems

Objective

To understand and solve linear systems.

System

A system of equations or inequalities is a set of open sentences each of which contains the same variables.

Solution Set

The solution set of a system with two variables is the set of all ordered pairs that satisfy all the open sentences in the system.

Chapter 4:Systems of Linear

Equations and Inequalities

Section 4-2:Solution of Systems of Linear

Equations

Objective

Given a system of two linear equations in two variables, solve it by transforming it to an equivalent system of the form:

x= constanty= constant

Example 1:

Solve the system:

2 10

3 9

x y

x y

Example 2:

Solve the system:

3 4 6

5 7 14

x y

x y

Example 3:

Solve the system:

5 2 10

5 2 20

x y

x y

Example 4:

Solve the system:

7 3 23

5 32

x y

x y

HOMEWORK: