Game Development Reference
In-Depth Information
You can now put this rewritten version of B to work to eliminate the
y
variable
from equation C. To accomplish this, you multiply B by
9 because 9 is the value
of the coefficient of
y
in equation C. Here is how your work proceeds:
9
y
10
z ¼
29
C
Start with C from STEP 2
:
3
2
z ¼ð
9
Þð
4
Þ
ð
9
Þy ð
9
Þ
B
Multiply B by
9
:
27
2
z ¼
36
9
y þ
B
Simplify B
ð
9
Þ:
7
2
z ¼
7
C
Add B
ð
9
Þ
to C
:
To solve equation C for
z
at this point, you use these steps:
7
2
z ¼
7
2
7
2
7
C
Remove the coefficient
:
14
7
z ¼
C
The coefficient of
z
is 1
:
z ¼
2
z
is known
:
C
STEP 3
The system now takes this form:
x
2
y þ
3
z ¼
11
A
Need to isolate
x
:
3
2
z ¼
4
y
B
Need to isolate
y
:
z ¼
2 C
z
is known
:
Given that you have identified the value of
z
, you can now use your knowledge to
eliminate the
z
variable from equations A and B. To accomplish this, you first
work with equation B. Then you work from there to equation A.
3
Beginning with equation B, then, given that the coefficient of
z
is
2
, you
multiply equation C by
2
to arrive at an equation you can add to B to eliminate
z
.
