Game Development Reference
In-Depth Information
If you consider the two equations that generate these lines, you end up with a
system that has this appearance:
x y ¼
3
x y ¼
3
If you try to arrive at a solution for this system of equations, you might proceed
by multiplying by
1 so that you can eliminate the
x
variable. Your work pro-
ceeds along the following lines:
x y ¼
3
x
þ
y
¼
3
Given this result, you can then add
x þ y ¼
3 to the first equation:
x y ¼
3
x þ y ¼
3
0
þ
0
¼
6
The addition operation produces an equation that is inconsistent because 0 is not
equal to 6. As it is, when you attempt to find values that allow you to create a
consistent addition product, your efforts fail. The system does not allow the lines
to intersect, so no solution exists.
Exercise Set 11.4
Determine which of these equations creates parallel lines.
a. 6a þ 4b ¼ 15
a þ 2b ¼ 12
b. a 3b ¼ 1
2a þ 6b ¼ 5
c. 6x 12y ¼ 16
3x 4y ¼ 8
d. y ¼3x þ 5
y ¼3x 2
e. 3y 2x ¼ 6
12y þ 8x ¼24
