Game Development Reference
In-Depth Information
2, so you can multiply equation B by 2 to arrive at an equation you can add to
equation A to eliminate the
y
variable. Here is how you proceed:
x
2
y ¼
5
A
Start with A from STEP 4
:
2
y ¼ð
2
Þ
1
B
Multiply B by 2
:
2
y ¼
2
B
Simplify B
:
x ¼
3
A
Add B to A
:
STEP 5
With the isolation of
x
, you now have values for all three of the variables in the
equation. You can show them as follows:
x ¼
3
A
x
is known
:
y ¼
1B
y
is known
:
z ¼
2 C
z
is known
:
To write the solutions for the original set of equations, you can employ par-
entheses in which you list the solutions in the order
x
,
y
, and
z
:
ð
3,
1, 2
Þ
Exercise Set 11.6
Solve the systems of equations.
a. 2x þ y þ z ¼2
2x y þ 3z ¼ 6
3x 5y þ 4z ¼ 7
b. 2x 3y þ z ¼ 5
x þ 3y þ 8z ¼ 22
3x y þ 2z ¼ 12
c. x þ 2y þ c ¼ 1
7x þ 3b z ¼2
x þ 5y þ 3z ¼ 2
d. a þ b þ 0c ¼ 0
a þ 0b þ c ¼ 1
2a þ b þ c ¼ 2
e. a þ b þ c ¼ 6
2a b þ 3c ¼ 9
a þ 2b þ 2c ¼ 9
