Game Development Reference
In-Depth Information
Figure 11.1
One ordered pair can be a solution to two or more equations.
solving systems of equations in various ways. One way is to generate ordered
pairs, and then compare the ordered pairs to determine if any are the same for
both equations. Another approach involves generating graphs for the equations
that you plot on one Cartesian coordinate plane and then compare. If you are
working with linear equations, the point at which the lines intersect constitutes a
solution for the system of equations.
Any given equation is likely to generate an indefinite number of ordered pairs.
The ordered pair that a given equation generates is a solution set. As with any two
sets, if the sets share common elements, then the shared elements are known as
the intersection of the two sets. Consider this set of equations:
y x ¼
1
y þ x ¼
2
Given this set of equations, you can then ask whether a coordinate pair exists that
satisfies both equations. To apply the graphical approach to answering this
question, you can use Visual Formula to implement the equations and generate
graphs of them. To implement the equations in Visual Formula, you must
rewrite them in this way:
y ¼ x þ
1
y ¼
2
x
Figure 11.2 illustrates these equations as implemented in Visual Formula. For
both equations, you create two Value fields. In the top equation, you use the Add
menu item to position a plus sign between the fields. For the lower equation, you
