Chapter 3: Linear Systems and Matrices

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Presentation transcript:

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

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)

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.

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.

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

Infinitely many solutions: Lines coincide: consistent and dependent

No solution: Lines are parallel: inconsistent

Example 1: 5x – 2y = -10 2x – 4y = 12

Example 2: 6x – 2y = 8 3x – y = 4

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

HOMEWORK pg. 156; 4 – 14 even