1. 3.5 Solving systems of equations in three variables Main Ideas Solve systems of linear equations in three variables. Solve real-world problems using systems of linear equations in three variables.

2. Systems in Three Variables Equations use 3 variables. When equations are graphed they create an ordered triple (x, y, z). The graph of an equation in three variables, if all have a power of 1, is a plane. How can three planes intersect? One point (x, y, z) Infinitely many solutions (a line or the same plane) No solution (they have no point in common)

3. How to solve a system of 3 variables Step 1 Choose one variable to eliminate. Step 2 Eliminate that variable with two of the equations. Step 3 Eliminate that same variable with the third equation and one of the other original equations. Step 4 Use the equations created from steps 2 & 3 to write a system of two variables and solve. (Any method) Step 5 Solve for the eliminated variable by replacing your answers from step 4 into an original equation.

4. Solve the system of equations. x + 2y = 12 3y – 4z = 25 x + 6y + z = 20

5. Solve the system of equations. 4x – 3y – 2z = 8 x + 5y + 3z = 9 -8x + 6y + 4z = 2

6. Solve the system of equations. 8x + 12y – 24z = -40 3x – 8y + 12z = 23 2x + 3y – 6z = -10