Game Development Reference
In-Depth Information
Systems with Three Variables
When you deal with systems of three equations with three variables, you extend
the addition and multiplication activities you perform when you work with
systems of two equations with two variables. The goals and procedures remain
the same. Your task is to move through the equations, multiplying and adding so
that you can express the equations so that they identify the values of the con-
stituent variables.
To examine how to work with a system of three equations with three variables,
consider this system:
2
x
4
y þ
6
z ¼
22
A
4
x þ
2
y
3
z ¼
4
B
3
x þ
3
y z ¼
4
C
To make it easier to identify the equations, you can associate them with letters of
the alphabet. As you go, the letters allow you to continue to identify the equations
as you rewrite after performing operations involving addition and subtraction on
them.
STEP 1
For starters, the first goal involves examining the system to see if there is a
convenient way to isolate the
x
variable. Toward this end, you multiply equation
Aby
2
, eliminating the coefficient of
x
.
2
x
4
y þ
6
z ¼
22
A
Original version of A
:
1
2
ð
2
xÞ
1
2
ð
4
yÞþ
1
2
ð
6
zÞ¼
1
2
ð
22
Þ
1
2
:
A
Multiply A by
x
2
y þ
3
z ¼
11
A
Simplify A
:
4
x þ
2
y
3
z ¼
4
B
Not changed
:
3
x þ
3
y z ¼
4
C
Not changed
:
If you examine equation B, you see that you can multiply the new form of
equation A by
4 to obtain an equation that eliminates the
x
variable from
