3.4 “Solving Linear Systems with 3 Variables”

The solutions are called an ordered triple (x,y,z). Equations are in the form of Ax + By + Cz = D.

1. 4x + 2y + 3z = 1 2x – 3y + 5z = -14 6x – y + 4z = -1

Steps:1. Number the equations 1,2,3.2. Make an elimination plan BEFORE

you start.3. Put 2 equations together and

eliminate a variable to get the first equation.

4. Put 2 DIFFERENT equations together and eliminate SAME variable to get the other equation.

5. Put the 2 equations together and solve by substitution or elimination.

6. Plug these answers in to one of the original equations to find the final variable.

7. Put the answer in ordered triple form.

Another Example:

2. 2x + 3y + 2z = 14 4x + 2y – z = 15 x + y + 3z = 8

Show all work, follow steps.

Try This:

3. 3x + y – 2z = 10 6x – 2y + z = -2 x + 4y + 3z = 7

Show all work, follow steps.

Another Example:4. x + y + z = 3 4x + 4y + 4z = 7 3x – y + 2z = 5

Show all work, follow steps.

Tell if a Point is a Solution:4. Is (1, 4, 3) a solution to the following problem? 2x – y + z = -5 5x + 2y – 3z = 19 x – 3y + z = -5

Plug in values for x, y, and z to see if it is true for ALL the equations.

Word Problem 1. TV World had a sell on televisions. On the first day, 4 projector, 10 flat screen, and 20 hand-held televisions were sold. On the second day, 2 projectors, 30 flat screens, and 30 hand-held televisions were sold. On the third day, 3 projectors, 15 flat screen, and 25 hand-held televisions were sold. The total sales for the three days were $10,400; $16,200; and $12,300. What was the sale price for each type?

Set up the equations and solve.