Game Development Reference
In-Depth Information
you proceed as follows:
4
þ y ¼
12
y ¼
12
þ
4
y ¼
16
Given the solution to
y
, you then have at hand the ordered pair (
4, 16). You can
test the validity of this ordered pair by substituting its two values into the
equations:
4
þ
16
¼
12
12
¼
12
Likewise, with the second equation,
16
¼
12
ð
4
Þ
16
¼
16
Exercise Set 11.1
Use substitution to solve these systems of equations for the value of x and y. Check your answers.
a. 6x 2y ¼4
3x þ 4y ¼ 1
b. 4x þ 6y ¼6
4x þ 4y ¼ 16
c. x 6y ¼ 4
2x 2y ¼ 7
d. 3x 2y ¼ 7
1
2
x þ y ¼
e. 2x þ y ¼ 6
3x þ 4y ¼ 4
Systems Solved by Adding and Multiplying
In addition to graphing the results of equations and using the substitution
method, you can also solve equations with a method that involves using mul-
tiplication and addition processes to eliminate variables from the equations. To
use this approach, you first assess the system of equations to determine a value by
