1. 3-Variable Systems
Algebra II
Unit 1

2. Review of Solving 2-Variable Systems
Method of Elimination
Solve for x and y:
Method of Substitution

3. 3-Variable Systems Solution is the ordered triple (x, y, z)
Can use the same methods as with 2-variable systems (substitution and elimination)

4. Example 1:    2a + (b – 15) = –10 2a + b = 5
Use  and substitute into 
2a + (b – 15) = –10
2a + b = 5
And substitute  into 
a – 2b + b – 15 = –5
a – b = 10
SOLUTION: (5, -5, -20)

5. Example 2:
Solution: (7, 4, –5)

6. Example 3: Write a system of equations to model the scenario.
At the 2000 Summer Olympics in Sydney, Australia, the United States won 97 medals. They won 6 more gold medals than bronze and 8 fewer silver medals than bronze.
Define your variables: g = number of gold medals
s = number of silver medals
b = number of bronze medals
2. Write your equations:
The United States won 97 medals
They won 6 more gold than bronze
They won 8 fewer silver than bronze

7. Word Problems Solve the problem from Example 3. 39 gold medals
25 silver medals
33 bronze medals