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