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: TablesHow?

Example 1a:Use a table to solve the system:

y=2x-3y=x+1

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

Classifying Systems:Lines intersect at one point-one solution

Consistent-at least one solutionIndependent-Exactly one solution

Lines coincide-infinite solutionsConsistent-at least one solution

Dependent-infinitely many solutions

Lines are parallel-No solutionInconsistent

Example 2:

Solve the system and classify:6x-2y=83x-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?

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