3-6 Systems with 3 VariablesObjectives:• To solve systems in 3 variables by elimination.• To solve systems in 3 variables by substitution.

System of 3 Variables• Can be

represented as graphs in 3 dimensions.• Solutions can be

shown graphically as the intersection of planes.• Solutions

represented as one point

Example 1: Solve each system by elimination.a)

Trivia…

1) Which athlete has won the maximum number of gold medals at a single Olympics?

Michael Phelps; 8 Gold Medals in Beijing 2008

Example 1: Solve each system by elimination.b)

Practice• WS – Elimination

When using Elimination of 2 variables, we sometimes have to multiply. The same is true for systems of 3 variables.

Example 2: Solve each system by elimination.a)

Trivia…

2) In which year did the Titanic sink?

1912

Example 2: Solve each system by elimination.b)

Practice• WS – Elimination (w/ Multiplying)

Substitution Method

• Best used when• One or more equations are solved for a

variable.• One equation can easily be solved for a

variable.

Example 3: Solve each system by substitution.a)

Example 3: Solve each system by substitution.b)

Trivia…

3) What is the #1 USA box office movie?

Avatar

Example 4: Write a system of 3 variables and then solve.Suppose you saved $3200 from a part time job and you want to invest your savings in a growth fund, an income fund, and a money market fund. Refer to the graph. To maximize your return, you decide to put twice as much money in the growth fund as in the money market fund. How should you invest the $3200 to get a return of $250 in one year?

Practice• WS –Substitution

Homework