Warm Up

•1.) Find the x – intercept of the graph of y = |x + 1|.

•2.) Express the cost C of x ball game tickets at a price of $18 per ticket.

3.1 Solve Linear Systems by GraphingAlgebra II

Objective

•Solve systems of linear equations.

Vocabulary

•System of two linear equations – 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 of a system – is an ordered pair (x, y) that satisfies each equation.

Example 1 – Solve a system graphically•Graph the linear system and estimate the

solution. Then check the solution algebraically.

•5x – 2y = -10•2x – 4y = 12

More Vocabulary• Classifying systems

• Consistent – a system with at least one solution.

• Inconsistent – a system with no solution.

• Independent – a consistent system that has exactly one solution

• Dependent – a consistent system with infinitely many solutions

Number of Solutions of a Linear System• The relationship between the graph of a linear

system and the system’s number of solutions is described below.

• 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 2 – Solve a system with many solutions•Solve the system. Then classify the

system as consistent and independent, consistent and dependent, or inconsistent.

•6x – 2y = 8

•3x – y = 4

Example 3 – Solve a system with no solution•Solve the system. Then classify the

system as consistent and independent, consistent and dependent, or inconsistent.

• -4x + y = 5

•-4x + y = -2

Assignment

•Pg. 156 (10 – 14 even, 18 – 24 even)