3-Variable Systems Algebra II Unit 1

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

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

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)

Example 2: Solution: (7, 4, –5)

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

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