# 01 Systems of Equations

A **system of linear equations** is a collection of linear equations with some variables in common, such as

where all $a$’s and $b$’s are known, and $x$’s are unknown.

- Solution
- All $x$'s that solve every equation simultaneously
- Solution Set
- The set of all possible solutions to the system.

Two systems are equivalent if the solution sets are equivalent.

## Three possibilities for the solution set

- No solutions
- Same slope, parallel lines
- One unique solution
- Lines cross once
- Infinitely many solutions
- Equivalent Systems