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Published byCameron Oliver Modified over 7 years ago
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 Graphing Algebra 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)
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