1. Chapter 3: Linear Systems and Matrices
Section 3.1: Solving Linear
Systems by Graphing

2. System of linear equations – in two variables x and y, also called a linear system, consists of two equations that can be written in the following form. Ax + By = C (Equation 1) Dx + Ey = F (Equation 2)

3. Solution – a solution of a system of linear equations in two variables is an ordered pair (x, y) that satisfies each equations. Solutions correspond to points where the graphs of the equations in a system intersect.

4. Consistent – a system that has a least one solution
Consistent – a system that has a least one solution. Inconsistent – if a system has no solutions. Independent – a consistent system with exactly one solution. Dependent – a consistent system that has infinitely many solutions.

5. Number of Solutions of a Linear System
Exactly one solution: Lines intersect at one point: consistent and independent.

6. Infinitely many solutions: Lines coincide: consistent and dependent

7. No solution: Lines are parallel: inconsistent

8. Example 1: 5x – 2y = -10 2x – 4y = 12

9. Example 2: 6x – 2y = 8 3x – y = 4

10. Example 3: -4x + y = 5 -4x + y = -2

11. HOMEWORK
pg. 156; 4 – 14 even