1
Created by Boundless
Solve the following system of equations using substitution: 3y-2x=11 and y+2x=9.
A
x=2 and y=5
B
x=3 and y=7
C
x=9 and y=11
D
x=5 and y=2
2
Created by Boundless
At a local animal shelter, the supplies for each dog costs twice as much as the
supplies for a cat. We need to feed 164 cats and 24 dogs, with a budget of $4240.
How much can we spend on each dog?
A
$50
B
$40
C
$60
D
$20
3
Created by Boundless
Solve the following system of equations using elimination: x − 2y
x + 3y = 9 .
A
x = 1
B
x =
and y
=
−12
−1 and y = 12
= 14
and −1
C
x = 12
and y
=
D
x = 12
and y
= 1
4
Created by Boundless
What resulting equation could we get if we eliminated the y variable in the
following system of equations: 2x + y = 9 and 3x − y = 16 ?
A
5x = 25
B
6x = 144
C
6x = 68
D
x = 7
5
Created by Boundless
Ben rides the Ferris wheel 3 times and goes down the water slide 3 times. Jeff also
rides the Ferris wheel 3 times but only goes down the water slide twice. Ben
spends $17.70 and Jeff spends $15.55. How much does the water slide cost per
ride?
6
A
$2.15
B
$3.75
C
$3.15
D
$2.75
Created by Boundless
What could we substitute in for y in the following system of equations: 2x-3y=-2
and 4x+y=24?
A
y=-4x+24
B
y=2x+2/3
C
y=2x+3
D
y=4x+24
7
Created by Boundless
Which of the following is a TRUE statement?
A
If two lines are perpendicular, then there is no solution of
the system.
B
If two lines intersect at (3, 4) , we say that x
y = 3 are solutions of the system.
C
If two lines are parallel, there are an infinite number of
solutions for the system.
D
A system in which two lines intersect at one point will have
only one solution.
8
= 4
and Created by Boundless
Solve the following system of equations graphically: 4x − 6y
2x + 2y = 6 .
A
x = 3
and y
= 0
B
x = 0
and y
= 3
C
x =
D
x = 0
−3 and y = 0
and y
=
−3
= 12
and y =
9
−3
Created by Boundless
Solve the following system of equations: ⎧ x + 2y + 6z = 5
⎪
⎨
x + y
2z = 3
⎪
⎩ x
4y
2z = 1
−
−
A
B
−
−
⎧x = 5
⎪
⎨ y = 8
⎪
⎩ z = 4
⎧ x = 1
⎪
⎨y =
2
⎪
⎩ z = 0
−
C
There are infinitely many solutions.
D
There is no solution (inconsistent).
10
Created by Boundless
The admission fee at a museum is $1.50 for children and $4.00 for adults. On a
Saturday, 2200 people entered the museum and $5050 was collected. How many
children and how many adults went to the museum on Saturday?
11
A
1800 children and 400 adults
B
1600 children and 600 adults
C
1500 children and 700 adults
D
1900 children and 300 adults
Created by Boundless
−
Solve the following system of equations: A
⎧ x + 2y
z = 4
⎪
⎨ 2x + y + z =
2
⎪
⎩ x + 2y + z = 2
−
−
⎧x =
5/3
⎪
⎨ y = 7/3
⎪
⎩ z =
1
−
B
⎧ x = 5/3
⎪
⎨y =
7/3
⎪
⎩
z = 1
−
C
D
12
−5/3
−7/3
−1
⎧x =
⎪
⎨y =
⎪
⎩ z =
⎧ x = 5/3
⎪
⎨ y = 7/3
⎪
⎩ z = 1
Created by Boundless
A test has twenty questions worth 100 points. The test consists of True/False
questions worth 3 points each and multiple choice questions worth 11 points
each. How many multiple choice questions are on the test?
13
A
10
B
5
C
20
D
15
Created by Boundless
−
Solve the following system of equations: A
B
⎧
3x
2y + 3z = 8
⎪
⎨ x + 3y + 6z =
3
⎪
⎩ 2x + 6y + 12z =
6
There is no solution (inconsistent).
−
⎧x =
3
⎪
⎨ y = 8
⎪
⎩ z =
6
−
C
D
14
There are infinitely many solutions.
−
−
⎧ x =
3
⎪
⎨y =
1/3
⎪
⎩
z = 0
Created by Boundless
Which of the following systems is dependent?
A
2x+3y=6 and 3x+5y=9
B
2x+3y=6 and 3x+4y=7
C
2x+3y=6 and x+2y=5
D
2x+3y=6 and 4x+6y=12
15
Created by Boundless
Which of the following systems is inconsistent?
A
x+3y=3 and 2x+6y=6
B
None of these answers.
−
−
C
2x+3y=6 and 4x+9y=15
D
2x+2y=5 and -2x-2y=3
16
Created by Boundless
Which of the following matrices represents a matrix in row echelon form?
A
0
1
4
[ 1
5
2]
B
B =
2
3
4
[ 0
5
2]
C
D
17
1
3
4
[ 0
1
2]
Created by Boundless
Suppose we have the following matrix: . Which of the following matrices is
equivalent to this matrix and is in row echelon form?
A
B
⎡ 1
⎢
0
⎢
1
1
1
1
⎣ 0
0
1
1⎦
⎡ 1
0
3
5
2
2
⎢
C
1⎤
⎥
1
⎥
⎤
⎥
⎢ 0
1
1
2 ⎥
⎣ 0
0
1
1 ⎦
None of these answers.
D
⎡ 0
0
1
1 ⎤
0
1
1
2
⎣ 1
0
3
5
2
2
⎢
⎢
18
⎥
⎥
⎦
Created by Boundless
Which of the following matrices is in reduced row echelon form?
A
B
C
D
19
⎡ 0
⎢
0
⎢
0
1
5⎤
⎥
3
⎥
1
0
⎣ 1
0
0
1⎦
⎡ 1
⎢
0
⎢
0
0
1
0
5⎤
⎥
3
⎥
⎣ 0
0
0
1⎦
⎡ 1
⎢
1
⎢
0
0
0
0
5⎤
⎥
3
⎥
⎣ 1
0
0
1⎦
⎡ 0
⎢
0
⎢
0
1
0
1
5⎤
⎥
3
⎥
⎣ 0
0
1
1⎦
Created by Boundless
Suppose we have the following matrix: ⎡1
⎢
⎢2
1
1
3
5
5⎤
⎥
8⎥
⎣4
0
5
2⎦
. Which of the following
matrices is equivalent to this matrix and is in reduced row echelon form?
A
⎡ 1
⎢
0
⎢
1
1
1
3
⎣ 0
0
1
5
⎤
⎥
−2 ⎥
−2 ⎦
B
C
⎡ 1
⎢
0
⎢
0
0
3
1
0
4
⎣ 0
0
1
⎡ 1
⎢
0
⎢
⎣ 0
D
20
⎤
⎥
⎥
−2 ⎦
1
1
1
3
−4
1
5
⎤
⎥
−2 ⎥
−18 ⎦
−5 ⎤
⎡ 1
⎢
0
⎢
0
0
1
0
3
⎣ 0
0
1
7
⎥
⎥
⎦
Created by Boundless
Which of the following represents the proper order one must take when operating
with elementary row operations?
A
Pivot, scale, swap.
B
The order does not matter.
C
Swap, scale, pivot.
D
Scale, pivot, swap.
21
Created by Boundless
Suppose we have the following matrix: . Which of the following matrices is
equivalent to matrix A?
A
B
C
None of these answers.
D
22
Created by Boundless
Solve: +.
A
B
C
D
23
Created by Boundless
Solve: .
A
B
−10
[
2
4
−6 ]
C
D
24
Created by Boundless
Multiply: .
A
B
[ 89
64 ]
[ 46
98 ]
[
]
C
D
25
Created by Boundless
Multiply: .
A
1
[ 3
2
4]
B
C
These matrices cannot be multiplied together.
D
26
Created by Boundless
Which of the following represents a matrix equation for the following system:
x+y+z=6, 2y+5z=-4, 2x+5y-z=27?
A
⎡ 1
⎢
0
⎢
1
⎣ 2
5
1⎦
⎡ 1
⎢
0
⎢
1
1
⎣ 2
5
2
1⎤
⎥
5
⎥
∗
⎡x⎤
⎡ 6 ⎤
⎢
⎥
⎢
⎥
=
y
4
⎢
⎥
⎢
⎥
⎣ z⎦
⎣ 27 ⎦
B
C
D
2
5
⎤
⎥
⎥
−1 ⎦
∗
⎡x⎤
⎡
⎢
⎥
⎢
=
y
⎢
⎥
⎢
⎣ z⎦
6
⎤
⎥
−4 ⎥
⎣ −27 ⎦
27
Created by Boundless
Which of the following represents a solution for the following system: x+y+z=6,
2y+5z=-4, 2x+5y-z=27?
A
x=1, y=2, z=3
B
x=0, y=3, z=-2
C
x=5, y=3, z=-2
D
x=-2, y=5, z=3
28
Created by Boundless
Use inverse matrices to solve the following system of linear equations: x+3y=6, x2z=-1, and 3y+z=5.
A
x=6, y=1, z=-3
B
x=2, y=1, z=3
C
x=3, y=1, z=2
D
x=4, y=5, z=2
29
Created by Boundless
Which of the following represents an identity matrix?
A
B
C
D
30
Created by Boundless
Which of the following matrices is the inverse of ?
A
B
C
−4
[ −3
−3
−2 ]
D
31
Created by Boundless
Which of the following matrices is the inverse of ?
A
⎡ 1
⎢
0
⎢
⎣ 0
1
0
0⎤
⎥
0
⎥
1⎦
B
C
D
32
Created by Boundless
Use Cramer's Rule to solve for z in the following system: 2x+y+z=3, x-y-z=0,
x+2y+z=0.
A
-2
B
0
C
1
D
3
33
Created by Boundless
Find the cofactor matrix of: A
12
−5
−3
⎣
2 5
−2 ⎥
−4 ⎦
⎡
24
5
−4 ⎤
⎡
⎢
⎢
B
−24
⎢
−12
⎣ −2 ⎢
C
D
⎡ 24
⎢
12
⎢
5
⎣ 2 5
−24
−12
⎢
⎣ −2 ⎡
⎢
34
3
4
⎡1
⎢
⎢0
2
4
3⎤
⎥
5⎥
⎣1
0
6⎦
⎤
⎥
3
2
−5
4
⎥
⎥
⎦
4⎤
⎥
2
⎥
4⎦
−5
−3
−5
−4 ⎤
⎥
−2 ⎥
−4 ⎦
Created by Boundless
Find the determinant of the following matrix: .
A
-14
B
14
C
36
D
50
35
Created by Boundless
Use Cramer's Rule to solve for y in the following system: 2x+y+z=3, x-y-z=0,
x+2y+z=0.
A
-2
B
1
C
0
D
3
36
Created by Boundless
Use Cramer's Rule to solve for x in the following system: 2x+y+z=3, x-y-z=0,
x+2y+z=0.
37
A
0
B
1
C
3
D
-2
Created by Boundless
Find the determinant of the following matrix: .
A
-54
B
36
C
-18
D
-306
38
Created by Boundless
Find M13 of the following matrix: A
-10
B
-2
C
0
D
2
39
⎡3
⎢
⎢2
0
⎣0
1
0
2
⎤
⎥
−2 ⎥
1
⎦
Created by Boundless
If the inequality y<2x+3 was graphed, which of the following points would fall in
the shaded region?
A
(-4,1)
B
(1,7)
C
(1,4)
D
40
(-1,4)
Created by Boundless
If the system 2x-y>-3 and 4x+y<5 was graphed, which of the following points
would fall in the shaded region?
A
(0,4)
B
(4,0)
C
(-2,0)
D
(0,2)
41
Created by Boundless
For the following system of linear inequalities, which of the following points falls in
the shaded region: 2x-3y<12, x+5y<20, x>0?
A
(2,6)
B
(6,2)
C
(2,-6)
D
(6,-2)
42
Created by Boundless
Why would one would choose to solve a system of inequalities using a nongraphical method?
A
There are too many variables.
B
All of these answers.
C
Graph paper is not available.
D
There are too many inequalities.
43
Created by Boundless
Find the maximum value of z=3a+2b+4c subject to the following constraints:
3a+2b+5c≤18, 4a+2a+3c≤16, and 2a+b+c≥4.
A
z=19
B
z=17
C
z=18
D
z=16
44
Created by Boundless
Express 7x
x
2
−23
−7x+12
in partial fractions.
A
B
2
x
C
−3
−44
x+3
D
44
x+3
45
−
+
−
5
x
−4
51
x+4
51
x+4
Created by Boundless
What is the result when we decompose A
2
x+2
B
3
x
C
D
−2
+ x−3 1
2
+ x+1
+
3
x+2
+
−4
into its partial fractions?
−x−2
5x
x
2