Game Development Reference
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for x . Accordingly, you might proceed in this way:
4 x þ 6 y ¼ 2
4 x
4 þ
6 y
4 ¼
2
4
3 y
2 ¼
1
2
x þ
1
2
3 y
2
x ¼
1 3 y
2
Given this finding, you can identify an ordered pair by using the value you
possess for the y variable. This takes the following form:
x ¼
1 3 y
2
, y
Working from this basis, you can proceed to furnish any value you choose for y
to arrive at the value of x . In this way, you can potentially generate an infinite
number of ordered pairs. Among these are the following:
ð 13
5
2 ,2
ð 4
;
3 Þ
;
9 Þ
Exercise Set 11.5
Explore these systems of equations and determine if they are dependent.
1
3 þ
1
4 ¼
1
16
a.
1
6 þ
1
2 ¼
12
16
b. 6x þ 5y ¼ 22
18x þ 15y ¼ 32
c. 4x þ 2y ¼ 20
24x þ 12y ¼ 8
d. 3y 2x ¼ 6
12y þ 8x ¼24
e. y ¼3x þ 5
y ¼3x 2
 
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