**Objectives**

- Solve literal equations with two variables.
- Rearrange formulas to solve for a quantity of interest in a real-world problem.
- Describe the steps in solving equations.
- Use units to guide and interpret your solutions of literal equations and formulas.

**Key Terms**

- Formula – an equation that describes an important mathematical relationship.
- Literal Equation – an equation that involves two or more variables.

**Notes**

- If you have two variables, you can solve for either one of them using reverse operations, even without having a value to substitute
- Example: Fahrenheit and Celsius are ways to tell the temperature. In the USA, we use Fahrenheit. In Europe, they use Celsius.
- Here is the formula for finding Celsius:
- What if you wanted to solve for Fahrenheit instead? Try solving for F by doing inverse (reverse) operations until you isolate the F.
- Step 1: Multiply by 9 on both sides
- and this will give you:

- Step 2: Divide by 5 on both sides
- and this will give you:

- Step 3: Add 32 to both sides
- You get the formula for finding Fahrenheit:
- If you want, you can rewrite it as

- Step 1: Multiply by 9 on both sides

- Example: Substitution
- Find x when y = 6 in the literal equation 5x + 4y = 39
- Step 1: Write with substitution: 5x + 4(6) = 39
- Step 2: Simplify: 5x + 24 = 39
- Step 3: Isolate the variable by subtracting 24 from both sides, THEN by dividing by 5 on both sides.
- Answer: x = 3

- Example: Inequality setup
- Question: Maya is taking her friends to a concert. Each ticket costs $25, and souvenir T-shirts are $12 each. There is a $4 service fee for the entire purchase. She has $130. If she buys 3 tickets, how many T-shirts can she buy?
- Given: x = number of tickets and y = number of T-shirts. Set up the inequality.
- Take notes on what you have: Tickets: $25, T-Shirts: $12, Service Fee (one time) $4, Total Budget $130
- Answer: 25x + 12y + 4 ≤ 130