Game Development Reference
In-Depth Information
equation B. Along the same lines, if you multiply the new form of equation A by
3, you obtain an equation you can use to eliminate the
x
variable from equation
C. Here is the form your work assumes:
x
2
y þ
3
z ¼
11
A
From the previous rewriting
:
4
x þ
2
y
3
z ¼
4
B
Original version of B
:
4
x þ
8
y
12
z ¼
44
A
Multiply A by
4
:
10
y
15
z ¼
40
B
Add A
ð
4
Þ
to B
:
Then you attend to equation C:
3
x þ
3
y z ¼
4
C
Original version of C
:
3
x þ
6
y
9
z ¼
33
A
Multiply A by
3
:
9
y
10
z ¼
29
C
Add A
ð
3
Þ
to C
:
STEP 2
You now have a system of equations in which you have eliminated the
x
vari-
able from two of the equations. You now need to isolate the
y
and
z
variables in
the same way. Here is the system of equations as you have rewritten them thus
far:
x
2
y þ
3
z ¼
11
A
Coefficient of x is 1
:
10
y
15
z ¼
40
B
Added A to remove
x
:
9
y
10
z ¼
29
C
Added A to remove
x
:
1
To proceed with the isolation of
y
in equation B, you multiply equation B by
10
.
In this way, you reduce the coefficient of
y
in equation B to 1. Here is the form
your work assumes:
10
y
15
z ¼
40
B
Start with B from STEP 2
:
15
10
z ¼
40
10
Multiply B by
1
y
B
10
:
3
2
z ¼
4
y
B
Rewrite to simplify
:
