Chapter 3 Linear Systems. 3.1 Solving Linear Systems What is a linear system?

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Presentation transcript:

Chapter 3 Linear Systems

3.1 Solving Linear Systems What is a linear system?

A system of two linear equations in two variables (x and y) Looks like:

What does it mean to solve a linear system?

What does a solution of linear systems look like?

How many ways can you solve a linear system?

Way #1: Tables How?

Example 1a: Use a table to solve the system: y=2x-3 y=x+1

Example 1b: Use a graph to solve the system: y=2x-3 y=x+1

Classifying Systems: Lines intersect at one point-one solution Consistent-at least one solution Independent-Exactly one solution Lines coincide-infinite solutions Consistent-at least one solution Dependent-infinitely many solutions Lines are parallel-No solution Inconsistent

Example 2: Solve the system and classify: 6x-2y=8 3x-y=4

Example 3: Solve the system and classify: -4x+y=5 -4+y=-2

A soccer league offers two options for membership plans. Option A includes an initial fee of $40 and costs $5 for each game played. Option B costs $10 for each game played. About how many games will the total cost of the two options be the same?

Check Solve the system and classify: -2x+y=5 y=-x+2