Game Development Reference
In-Depth Information
You can make it easier to work with this system of equations if you leave the
coefficient of
x
in the second equation unchanged and instead manipulate the
first equation. To make it possible to preserve the coefficient of
x
in the second
equation, you reverse the order of the equations. The second equation becomes
the first:
x
4
y ¼
1
4
x þ
2
y ¼
0
The changed order does not alter the value the equations generate. It only makes
it so you can work with them more readily. Given this reordering, then, you can
proceed with the elimination of the
x
variable.
Preliminary Multiplications
In some instances, you work with systems of equations that contain decimal
values. In such situations, if you inspect the decimal values, you might find that if
you multiply them by a power of 10 (10, 100, and so on), you can eliminate the
decimal values. Elimination of the decimal values makes it much easier to pro-
ceed as you work with multiplications you require to eliminate the
x
or
y
vari-
ables. Here is an example of a system of equations that contains decimal values:
0
:
4
x þ
0
:
6
y ¼
0
:
04
0
:
02
x
0
:
4
y ¼
1
:
4
For both of these equations, if you multiply by 100, you can eliminate the decimal
points and so arrive at terms that consist of integers. Your actions take the
following form:
0
:
4
x þ
0
:
6
y ¼
0
:
04
ð
multiply by 100
Þ
0
:
02
x
0
:
4
y ¼
1
:
4
ð
multiply by 100
Þ
This multiplication results in a new version of the system that preserves the value
relationship of the first:
40
x þ
60
y ¼
4
2
x
40
y ¼
140
Given this adjusted view of the system of equations, you can now proceed much
more readily toward a solution for the system.
