1. Linear Systems
Chapter 3

2. 3.1 Solving Systems Using Tables and Graphs
Pg. 134 – 141
Obj: Learn how to solve a linear system using a graph or a table.
A.CED.2, A.REI.6, A.REI.11, A.CED.3

3. 3.1 Solving Systems Using Tables and Graphs
System of Equations – a set of two or more equations
Linear System – a system that consists of linear equations
Solution of a System – a set of values for the variables that makes all the equations true
Inconsistent System – a system that has no solution – parallel lines
Consistent System – a system that has at least one solution
Independent System – a system that has exactly one solution – intersecting lines
Dependent system – a system that has infinitely many solutions – the same line

4. 3.2 Solving Systems Algebraically
Pg. 142 – 148
Obj: Learn how to solve systems algebraically.
A.REI.6, A.REI.5, A.CED.2

5. 3.3 Systems of Inequalities
Pg. 149 – 155
Obj: Learn how to solve systems of linear inequalities.
A.REI.12, A.REI.6, A.CED.3

6. 3.4 Linear programming Pg. 157-162
Obj: Learn how to solve problems using linear programming.
A.CED.3

7. 3.4 Linear programming Constraints – limits
Linear Programming – a method for finding a minimum or maximum value of some quantity, given a set of constraints
Feasible Region – the region that contains all the points that satisfy all the constraints
Objective Function – the quantity you are trying to maximize or minimize
Vertex Principle of Linear Programming
If there is a maximum or a minimum value of the linear of the linear objective function, it occurs at one or more vertices of the feasible region.

8. 3.5 Systems With three VariablesPg
Obj: Learn how to solve systems in three variables using elimination and substitution.
A.REI.6

9. 3.6 Solving Systems Using Matrices
Pg. 174 – 181
Obj: Learn how to represent and solve a system of linear equations using matrices.
A.REI.8

10. 3.6 Solving Systems Using Matrices
Matrix – a rectangular array of numbers
Matrix Element – each number in a matrix
Row Operation – each step used to solve a matrix
Row Operations
Switch any two rows
Multiply a row by a constant
Add one row to another
Combine any of the steps

11. 3.6 Solving Systems Using Matrices
Use row operations to convert matrices to the following form