# Unit 4

### Table of Contents

# Unit 4 - Linear Equations and Linear Systems

## Unit 4 Vocab

## Solving equations

### In fact, solving an equation is just like solving a puzzle. And like puzzles, there are things we can (and cannot) do.

#### Here are some things we can do:

- Add or Subtract the same value from both sides
- Clear out any fractions by Multiplying every term by the bottom parts
- Divide every term by the same nonzero value
- Combine Like Terms

## Number of solutions

- Most equations will have 1 solution.
- This looks like ** X = Some Number **
- This happens any time that the two sides of the equation have a different number of variable terms.
- 3x+5=9
- 3x+5=2x-4

- Some times an equation has a matching number of variable terms on each side. ðŸ””ðŸ””ðŸ””ðŸ””ðŸ””
- If the variables match then they will cancel out.
- 3x+5=3x+5
- 3x+5=3x+2

- In these special cases we must check the constant terms (The just numbers) on each side.
- If they match there are infinite solutions. This means any value for x will satisfy the equation.
- 3x+5=3x+5
- 2x=2x
- x+5 = x+5

- If they do not match there is no solution to the equation.
- 3x+5 = 3x+2
- 2x = 2x+5
- x+5 = x

- If they match there are infinite solutions. This means any value for x will satisfy the equation.

- If the variables match then they will cancel out.