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.
Steps:
1.
3.
4x + 2y + 3z = 1
2x – 3y + 5z = -14
6x – y + 4z = -1
1.
2.
4.
5.
6.
7.
Number the equations 1,2,3.
Make an elimination plan BEFORE
you start.
Put 2 equations together and
eliminate a variable to get the
first
equation.
Put 2 DIFFERENT equations
together and eliminate SAME
variable to get the other
equation.
Put the 2 equations together
and solve by substitution or
elimination.
Plug these answers in to one of
the original equations to find the
final variable.
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 handheld 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.