Algebra Trig
Chapter 2 Test Ieview
Name
tate
Write the letter of the correct answer for each of the following problems:
1. Which system is inconsistent? M,’Y)L L-J
y=O.5x
2x y =8
x + y =0
A.
B.
C.
x—2y=1
4x + y = 5
2x = y
—
Q
1.
5
S
2. Which system of equations is shown by the graph?
—3x+y=1
A.
B.
x+y=3
C.
3x—y=1
x+y=3
x+y=3
—6x+3y=—3
—x+y=1
3x—y=1
/
(, o)
-
3. Which term best describes the system shown in the graph?
Infeasible
Unbounded
A.
C.
B.
b.
Alternate Optimal
Optimal
Cc PA1&\
4. Solve algebraically:
2x+7y=5
6x+ y =5
S
-/2?C
(n
2JJ) ÷?y.= S
+
L=Z
I$susss
sass
‘ma
1c,
1K
1
y=—
x=2
g
5. Solve algebraically:
%j/
6x—3y+8z=4
x+ 9y 2z = 2
1-33(’3)I2
2X
—
—
4x+6y—4z=3
fr
-I-I1ta
2-X
cD4-2
X”a
rX -1I2&1 —a=
I)
—
k)-q3
,Lfd/)
fo
z -1-2 -c.=-3
-J
-i--a
3rz2
-
6. Evaluate the following for the matrices:
a.
AB’
-32
hf
ABC
-q--/
-
L-7
b.
BC
d.
1
K
0
Ei —2
B=l
L 5
54
2 —1
C=
—1
3
10
-2,
-1Z
C.
A=[6 —4
2
1
jy
-,J
L’
7. Write the matrix equation for the following systems and solve:
2x—7y+z=5
—y+7x=14/7j ,
6x + y =5
b.
a.
—3x+z=11
r?
‘1F
JLJ
-
L’J
2
F
-7
‘5
iJLi
r7 ‘r’
JL
-7
I
L
z
J
I
2
1
i]
o
I_i
S.
[5
11
4
Z
‘‘7/
0; x +2
y
8. Which is the graph of the system:
A.’
30 —>
y
and 2x+3y9
jy]t/
v4fD.
B.
f f’il I
?i
1H T
1
trrHf
f(x,y)=2x—y+2
9. Find the minimum value of
1x3;
system of inequalities:
for the polynomial convex set determined by the
yO
(oo)
• X=3
and
,)
-
O—O-fr2
2_
4-’+2
(,o)
—D
—
(2, Va)
/
-2.
2..
-‘-
%/z.. + 2
qY.
J-’:(os)
x-LQ,ø)
-k*
x+y5
/
oçV
-i**I
yO; x0
6x + 3y 18
10. bescribe the linear programming situation for the system of inequalities and x 3y 9
+
f(x,y)=x+ y
where you are asked to find the maximum value of
o±o
(o)
.
o
(a)
Xz
=
-4y-
x-m(3
o
1
)
(ys /s)
3
Co
4
(O)
-
c
K--3=-
X--: ,o)
-4s+
9
j_((33)
ov
iS
)(:;
\
(L,4Li
1
7
j
11. Chase Quinn wants to expand his cut-flower business. He has 12 additional acres on which he intends
to plant lilies and gladioli. He can plant at most 7 acres of gladioli bulbs and no more than 11 acres of
lilies. Chase knows that the number of acres planted to gladioli can be no more than twice the number of
acres planted to lilies. In addition, the hours spent on lilies plus twice the hours spent on gladioli must be
at least 10 hours per day. If the profit earned is $300 for lilies and $200 for gladioli how many acres of
each should be planted to maximize profit?
) cYeS
&cI
-bLff
(
/;l 0
Co-4Q-d
f
tc r
\ \.
----is
E.
1
.
IZ.
cTh(+j
Aj
)2.
K-v f’2)
)cH
j=---) jx= I
;
x)
/
ID
O
)(+ 2
j= 10
X-tvm
(io,’)
--
(o,)
oo X
N+
pJ
3
1
D
‘j7
ZN
)
(3,7)
(7)
(37)
ooL3Vz2tô
2ttCs4 2OC’) $4z1Oc
ocC. I
‘
-
200
-7;
(ii,
(5,-?’)
x=’(
o)
3V(H) 3So
)(42
Stz( 2) -1-- 2D (.q)
®
-2..X;
2
:-tD
4
x
a_sz