Systems of Linear Equations in two Variables

1
Section 8.1
Systems of Linear Equations in two Variables
2
Purpose
1. To find an answer, answers or no answer that
the equations have in common. 2. The next few
sections will address the different methods to
solve for those answers. 3. The problem will
have a title called solving system of linear
equations. System represents the idea of more
than one. Linear Equation represents an
equation where the variables have a power of
one, only.
3
Methods

• Graphing Method Section 8.1
• Substitution Method Section 8.2
• Addition / Elimination Method Section 8.2
• Matrix Method Section 8.6
• Cramer's Rule Section 8.7

4
Graphing Method

• A visual way to find the solution(s)/point(s)
  they have in common.
• If the lines intersect, the point(s) where they
  intersect is(are) the answers.
• You will have some leeway on determining the
  point(s), sometimes it will be a guessing game.
• Definitions
• Consistent there is at least one solution
• Inconsistent there is no solution in common
• Dependent same line
• Independent not the same line

5
Graphing Method
6
Example
Solve the system of linear equations given,
7
Example
Solve the system of linear equations given,
8
Example
Solve the system of linear equations given,
9
Example
Solve the system of linear equations given,
10
Homework

• Section 8.1 18, 22, 25, 33, 35