Game Development Reference
In-Depth Information
The test for the second equation also shows the pair to be valid:
y þ x ¼
2
1
:
5
þ
0
:
5
¼
2
2
¼
2
Substitution
To solve a system of equations in a more systematic way, you use substitution.
Toward this end, you first solve one of the equations in the system for one of its
variables. You then substitute the solution into the other equation.
Here is a system of equations that you can solve in this way:
x þ y ¼
12
3
x þ y ¼
4
To solve this set of equations through substitution, you can solve either equation
for either variable. In this instance, begin by solving the first equation for
y
:
x þ y ¼
12
y ¼
12
x
You can then proceed to substitute the expression 12
x
into the second of the
equations. To do so, you proceed as follows:
3
x þ y ¼
4
3
x þð
12
xÞ¼
4
2
x þ
12
¼
4
2
x ¼
4
12
x ¼
8
2
x ¼
4
Having arrived at this solution for
x
, you can then return to either of the
equations in the system and solve for
y
. Accordingly, if you use the first equation,
