(
Show all your work
to get full credit
. This
quiz covers material
s
fr
om week 3
)
1.
(
10
pts)
Solve the linear equations:
a.
1
6
3
=
-
=
+
-
x
if
y
x
b
.
2
12
3
2
=
=
+
y
if
y
x
2.
(
3
0 pts)
Solve the system of linear equation by graphing.
a.
î
í
ì
<
-
³
+
4
2
2
y
x
y
x
b.
î
í
ì
³
-
£
-
0
4
2
6
2
y
x
y
x
3.
(
3
0 pts)
Solv
e the following linear programming
problems graphically.
a.
Maximize the objective function
y
x
P
+
=
2
Subject
to:
ï
ï
î
ï
ï
í
ì
³
+
£
+
³
³
1
6
0
0
y
x
y
x
y
x
b.
Minimize the objective function
3
2
+
=
x
C
Subject to:
ï
ï
ï
î
ï
ï
ï
í
ì
³
+
£
£
³
³
2
5
6
0
0
y
x
y
x
y
x
4
.
(3
0 pts)
Solve the system of equations
ï
î
ï
í
ì
=
-
+
=
+
+
=
+
13
4
3
1
6
2
2
z
y
x
z
y
x
y
x
by augmented matrix
Solve the system of equations
ï
î
ï
í
ì
=
+
-
=
+
+
-
=
+
2
3
4
3
4
3
3
z
y
z
y
x
y
x
by using inverse matrix
(Show all your work to get full credit. This quiz covers materials from week 3)
1. (10 pts) Solve the linear equations:
a. 163xifyx b. 21232yifyx
2. (30 pts) Solve the system of linear equation by graphing.
a.
42
2
yx
yx
b.
042
62
yx
yx
3. (30 pts) Solve the following linear programming problems graphically.
a. Maximize the objective function yxP2 Subject to:
1
6
0
0
yx
yx
y
x
b. Minimize the objective function 32xC Subject to:
2
5
6
0
0
yx
y
x
y
x
4. (30 pts) Solve the system of equations
1343
1
622
zyx
zyx
yx
by augmented matrix
Solve the system of equations
234
343
3
zy
zyx
yx
by using inverse matrix
jamex.a.bowher2s
UMUCQ3-Math106Fall17.docx
0
