Game Development Reference
In-Depth Information
which you can multiply one of the equations so that you can make one or another
of its coefficients the additive inverse of the corresponding coefficient in the
other equation. You then multiply by this value and carry out an addition
operation to arrive at a new equation in which you have eliminated one of the
variables. You repeat this process until you arrive at values for each of the
variables in the system.
To see how this works, consider this system of equations:
4
x
4
y ¼
1
4
x þ
2
y ¼
0
When you assess this system of equations, you can see that the coefficients of
x
are additive inverses. Since your goal is to arrive at a new equation in which you
eliminate one of the two variables, adding these two equations immediately
provides you with a desired result. When you carry out the addition, your activity
takes the following form:
4
x
4
y ¼
1
4
x þ
2y
¼
0
-- 2
y ¼
-- 1
The addition eliminates
x
as a variable and leaves youwith the equation
2
y ¼
1.
To find the value of
y
, you need to eliminate the coefficient of
y
, and to
accomplish this, you multiply the equation by
2
:
1
2
2
y ¼
1
The result of this activity is the value of
y
:
1
2
y ¼
This, then, provides you with half of your goal. Now that you have the value of
y
,
you can proceed with discovering the value of
x
. To discover the value of
x
, you
bring forward the first equation from the system of equations:
4
x
4
y ¼
1
Your goal this time around is to eliminate the coefficient of
y
. To accomplish this,
you make use of the fact that you know the value of
y
. The coefficient of y in the
equation is
4. You must multiply the equation that establishes the value of
y
by a
