1. 3.5 Solving Systems of Equations in Three Variables The student will be able to solve systems of linear equations in three variables algebraically.

2. When solving a system of equations in two variables, we represent the solution as an ordered pair (x, y). [Unless the solution has “no solution” or “infinitely many solutions”] When solving a system of equations in three variables, the solution is an ordered triple (x, y, z).

3. When graphing an equation with three variables, we no longer are graphing lines, but rather we are graphing planes. These graphs are three dimensional.

5. Steps for Solving a System of Equations in Three Variables 1)Decide which variable you want to eliminate. 1)Pick two equations. Use elimination to eliminate that variable. (You should then be left with an equation that contains the two variables you did not choose in step 1.) 2)Take one of the original equations you chose in step 2, in addition to the other original equation that was untouched in step 2. Use those two equations and again eliminate the variable you chose in step 1.

6. 4) You are now left with two equations that each contain the same two variables. Solve this system by using either elimination or substitution, just as we did in section 3-2. 5) Once you have a value for each of these two variables, pick one original equation and substitute these values in to find the value of the third variable. 6) If the system has one solution, write your ordered triple. If the system has no solution, or infinitely many solutions, state that.

7. Example 1: Solve the system of equations.

8. Example 2: Solve the system of equations.

9. Example 3: Solve the system of equations.

10. Your Turn! : Solve the system of equations. 4)5)

11. Homework Text p. 142 #s 6-8