Systems of Equations

1
Systems of Equations

• An Introduction

2
What are systems of equations?

• A system of equations is a set of two or more
  equations containing two or more variables.
• A solution of a system of equations with two
  variables is the set of ordered pairs that
  satisfies each equation in the system. (There
  usually is only one!)
• We will focus specifically on linear systems in
  this unit of study!

3
Different types of Systems

• The note sheet that you have in front of you
  describes three different types of systems. Your
  task is to take notes on the three different
  scenarios possible when solving a system of
  equations.

4
Inconsistent Systems

• equations with no common solutions
• expressed as
• no solution or S

The lines are parallel.
5
Independent Systems

• linear equations that intersect in just 1 point.
  
• Expressed as an order pair
• in set notation
• S (x, y)

S (2, 3)
6
Dependent Systems

• 2 equations with the same graph
• infinite number of solutions

Sreal numbers
7
Recall how to solve

• Solve the systems listed on your note sheet.
  When you are finished, you should have one
  example of each system.
• Remember there are three ways to solve a system

8
Solving Systems

• We will take a look at each of these in class
• Systems can be solved by graphing the system of
  equations.
• Systems can be solved by substitution where one
  equation is substituted into the other.
• Systems can be solved by a process of linear
  combinations (or elimination).
• Try either solving by substitution or linear
  combinations on the note sheet.

9
Linear Combinations

• Linearly combining process of multiplying 2
  variables by constants and adding the results.
  We will call this using linear combinations to
  solve a system