MAT 110 Palo Verde College Algerba Questions

Page 96 of 123LONG TEST # 5 MAT 110-06
(CHAPTER 9) ( 2 pts each)
DUE DATE: APRIL 15, 2022
1.
Use the method of substitution to solve the following system of equations. If the
system is dependent, express the solution set in terms of one of the variables. Leave all
fractional answers in fraction form.
{
A) Only One Solution
B) Inconsistent System
C) Dependent System
2.
−2𝑥
( ________
𝑦
5𝑦
= 38
= −6
, ________ )
{(________
, ________
) |________∈ ℝ}
Use the method of substitution to solve the following system of equations. If the
system is dependent, express the solution set in terms of one of the variables. Leave all
fractional answers in fraction form.
6𝑥
{
−2𝑥
A) Only One Solution
B) Inconsistent System
C) Dependent System
3.
+
( ________
−
5𝑦
=
=
−24
−42
, ________ )
{(________
, ________
) |________∈ ℝ}
Use the method of substitution to solve the following system of equations. If the
system is dependent, express the solution set in terms of one of the variables. Leave all
fractional answers in fraction form.
{
A) Only One Solution
B) Inconsistent System
C) Dependent System
2𝑥
4𝑥
( ________
{(________
+
+
9𝑦
2𝑦
=
=
5
−6
, ________ )
, ________
) |________∈ ℝ}
Page 97 of 123
4.
Use the method of substitution to solve the following system of equations. If the
system is dependent, express the solution set in terms of one of the variables. Leave all
fractional answers in fraction form.
{
A) Only One Solution
B) Inconsistent System
C) Dependent System
5.
5𝑦
10𝑦
=
=
18
34
, ________ )
{(________
, ________
) |________∈ ℝ}
Use the method of substitution to solve the following system of equations. If the
system is dependent, express the solution set in terms of one of the variables. Leave all
fractional answers in fraction form.
A) Only One Solution
B) Inconsistent System
C) Dependent System
𝑥
5𝑥
+
+
( ________
{(________
5𝑦
25𝑦
=
=
−9
−45
, ________ )
, ________
) |________∈ ℝ}
Use the method of elimination to solve the following system of equations. If the system
is dependent, express the solution set in terms of one of the variables. Leave all
fractional answers in fraction form.
{
A) Only One Solution
B) Inconsistent System
C) Dependent System
7.
−
−
( ________
{
6.
−𝑥
−2𝑥
−7𝑥
𝑥
( ________
{(________
−
+
8𝑦
6𝑦
=
=
−5
−9
, ________ )
, ________
) |________∈ ℝ}
Use the method of elimination to solve the following system of equations. If the system
is dependent, express the solution set in terms of one of the variables. Leave all
fractional answers in fraction form.
Page 98 of 123
{
A) Only One Solution
B) Inconsistent System
C) Dependent System
8.
−3𝑥
6𝑥
( ________
4𝑦
8𝑦
=
=
8
−19
, ________ )
{(________
, ________
) |________∈ ℝ}
Use the method of elimination to solve the following system of equations. If the system
is dependent, express the solution set in terms of one of the variables. Leave all
fractional answers in fraction form.
{
A) Only One Solution
B) Inconsistent System
C) Dependent System
9.
−
+
2𝑥
6𝑥
+
+
( ________
{(________
5𝑦
15𝑦
=
=
−11
−33
, ________ )
, ________
) |________∈ ℝ}
Use any convenient method to determine whether the following system of equations is
consistent, inconsistent, or dependent.
{
−𝑥
2𝑥
− 3𝑦
+ 6𝑦
=
=
−14
21
A) Only One Solution
B) Inconsistent System
C) Dependent System
10.
Use any convenient method to solve the following system of equations. If the system is
dependent, express the solution set in terms of one of the variables. Leave all fractional
answers in fraction form.
−2𝑥
{ 𝑥
3𝑥
+
+
+
𝑦
7𝑦
6𝑦
+ 2𝑧
− 3𝑧
− 5𝑧
=
=
=
16
3
−13
Page 99 of 123
A) Only One Solution
B) Inconsistent System
C) Dependent System
|________∈ ℝ}
11.
Answer: ( ________
Answer: {( ________
A) Only One Solution
B) Inconsistent System
C) Dependent System
|________∈ ℝ}
𝑥
+
−2𝑥
−
3𝑦
𝑦
5𝑦
−
+
Answer: ( ________
Answer: {( ________
, ________
, ________
)
2𝑧
4𝑧
= −10
= −9
=
5
, ________
, ________
, ________ )
, ________
)
Use any convenient method to solve the following system of equations. If the system is
dependent, express the solution set in terms of one of the variables. Leave all fractional
answers in fraction form.
2𝑥
{3𝑥
𝑥
A) Only One Solution
B) Inconsistent System
C) Dependent System
|________∈ ℝ}
13.
, ________ )
Use any convenient method to solve the following system of equations. If the system is
dependent, express the solution set in terms of one of the variables. Leave all fractional
answers in fraction form.
{
12.
, ________
−
+
−
10𝑦
6𝑦
5𝑦
+
−
+
Answer: ( ________
Answer: {( ________
4𝑧
5𝑧
2𝑧
= 17
= −5
= 9
, ________
, ________
, ________ )
, ________
)
Use a system of equations to solve the following problem.
How many ounces of a 19% alcohol solution and a 41% alcohol solution must be
combined to obtain 66 ounces of a 25% solution?
Page 100 of 123
Answer: _______________ounces of 19% alcohol solution
_______________ounces of 41% alcohol solution
14.
Consider the following matrix:
−1 −13
Let 𝐷 = [ 1
3
9 −10
−2
−5]
7
Step 1. Determine the order of 𝐷.
Answer: _______________ ×_______________
Step 2. Determine the value of 𝑑2 1 , if possible. If the element indicated is not in the
matrix, state “None”.
A) ____________
B) None
Step 3. Determine the value of 𝑑1 3, if possible. If the element indicated is not in the
matrix, state “None”.
A) ____________
15.
B) None
Consider the following matrix:
4
−45
−13 −46
Let 𝐴 = 11
31
−15
2
[−38 19 ]
Step 1. Determine the order of 𝐴.
Answer: _______________ ×_______________
Page 101 of 123
Step 2. Determine the value of 𝑎1 1, if possible. If the element indicated is not in the
matrix, state “None”.
A) ____________
B) None
Step 3. Determine the value of 𝑎4 2, if possible. If the element indicated is not in the
matrix, state “None”.
A) ____________
16.
B) None
Construct the augmented matrix that corresponds to the following system of equations.
3𝑥 + 4𝑦3− 𝑧
{3(4𝑧 − 5𝑥) + 𝑦 − 5
𝑥 − (6 + 𝑧)
=
=
=
4
6
5𝑦
Answer: ____________________
17.
Construct the augmented matrix that corresponds to the following system of equations.
5 + 8𝑥
5
{4𝑧 − 3(𝑥 − 4𝑦)
5𝑥 − 𝑦
=
=
=
𝑦
0
3(𝑥 − 6𝑧)
Answer: ____________________
18.
Fill in the blank by performing the indicated elementary row operation(s).
[
4 3 −1 −4𝑅2 + 𝑅1
| ]
1 1 −3 →
?
Answer: ____________________
19.
Use Gaussian elimination and back-substitution to solve the following system of
equations. If there is a solution, write your answer in the format (𝑥, 𝑦).
Page 102 of 123
{
𝑥
7𝑥
+
+
6𝑦
𝑦
=
=
−11
−36
A) No Solution
B) One Solution
Solution Set: (________ , ________)
C) Infinitely Many Solutions
Solution Set: {(________ , ________)
ℝ}
20.
Determine the minor of 𝑎1 2 in the matrix.
3 −3 2
𝐴 = [9 6 3]
7 5 0
Answer: _______________
21.
Determine the minor of 𝑎2 2 in the matrix.
2 −4 5
𝐴 = [2 3
9]
2 2 −4
Answer: _______________
22.
Determine the cofactor of 𝑎1 3 in the matrix.
2 −3 8
𝐴 = [4 7
8]
5 1 −6
Answer: _______________
23.
Determine the cofactor of 𝑎3 2 in the matrix.
|________∈
Page 103 of 123
1 −1 3
𝐴 = [7 7
5]
7 6 −5
Answer: _______________
24.
Evaluate the determinant of the matrix.
12
𝐴 = [
6
−12
]
−6
Answer: _______________
25.
Evaluate the determinant of the matrix.
−36
𝐴 = [
10
40
]
21
Answer: _______________
26.
Evaluate the determinant of the matrix.
2𝑎𝑐
𝐴 = [
2𝑏𝑐
4𝑎𝑑
]
2𝑏𝑑
Answer: _______________
27.
Given the following matrices, if possible, determine 𝐴 + 𝐵 + 𝐶. If not, state “Not
Possible”.
3 10
𝐴 = [−6 −7]
8
6
Answer: ____________________
−6 3
𝐵 = [ 8 −8]
−6 −5
−5 −6
𝐶 = [−8 −6]
9 −1
Page 104 of 123
28.
Given the following matrices, if possible, determine 3𝐴. If not, state “Not Possible”.
−4 −6
𝐴 = [1
1]
−7 −5
Answer: ____________________
29.
Given the following matrices, if possible, determine 3𝐵 − 4𝐴. If not, state “Not
Possible”.
−2 −6
𝐴 = [ 6 −8]
3
5
8
𝐵 = [
3
−2 −8
]
−7 −9
Answer: ____________________
30.
Given the following matrices, if possible, determine 4𝐴 − 4𝐵. If not, state “Not
Possible”.
𝐴 = [−9 −7 −2]
𝐵 = [0
1 −4]
Answer: ____________________
31.
Determine values of the variables that will make the following equation true, if possible.
If not, state “Not Possible”.
−2𝑎
3
2𝑎
4 [ ] + 2 [ 𝑏 ] = [−2]
𝑏
𝑐
−2
A) 𝑎 =__________𝑏 =__________𝑐 =__________
B) Not Possible
32.
Determine values of the variables that will make the following equation true, if possible.
If not, state “Not Possible”.
Page 105 of 123
2[𝑥
2𝑦
3𝑧 ] − 4[ 𝑥
3𝑦
2𝑧 ] = [2 64
10]
A) 𝑥 =__________𝑦 =__________𝑧 =__________
B) Not Possible
33.
Determine values of the variables that will make the following equation true, if possible.
If not, state “Not Possible”.
3[
4𝑤
3𝑦
4𝑥
3𝑤
] − 3[
𝑧
−2𝑦
3𝑥
𝑤 + 18
] = [
4𝑧
−105
−12
]
54
A) 𝑤 =__________𝑥 =__________𝑦 =__________𝑧 =__________
B) Not Possible
34.
Write the following system of equations as a single matrix equation.
{
4𝑦 +
−5 +
13 =
𝑥 =
−8𝑥
2𝑦
Answer: ____________________
35.
Write the following system of equations as a single matrix equation.
3𝑥
{
−
𝑦
8𝑥
2𝑦
+
+
−
5𝑧
9𝑦
9𝑧
= −2
= −5
= 12
Answer: ____________________
36.
Write the following system of equations as a single matrix equation.
{
6𝑧 − 7𝑥
6𝑦
𝑥 + 9𝑦 − 14
=
=
=
0
−12 + 3𝑧
0
Page 106 of 123
Answer: ____________________
37.
Find the inverse of the following matrix, if possible. Reduce all fractions to lowest
terms.
−3 7
𝐴 = [
]
−1 3
Answer: ____________________
38.
Find the inverse of the following matrix, if possible. Reduce all fractions to lowest
terms.
2 −3
𝐴 = [
]
−5 5
Answer: ____________________
39.
Find the inverse of the following matrix, if possible. Reduce all fractions to lowest
terms.
−5 −7
𝐴 = [
]
10 14
Answer: ____________________
40.
Find the inverse of the following matrix, if possible. Reduce all fractions to lowest
terms.
−3 −6 −3
𝐴 = [1
6
1]
−2 3 −2
Answer: ____________________
41.
Solve the system of two linear inequalities graphically.
𝑥 > 7
{
𝑦 ≥ 2
Page 107 of 123
Step 1. Graph the solution set of the first linear inequality.
Step 2. Graph the solution set of the second linear inequality.
Step 3. Graph the solution set for the system.
Page 108 of 123
42.
Solve the system of two linear inequalities graphically.
𝑦 < 2 { 𝑦 ≥ −1 Step 1. Graph the solution set of the first linear inequality. Step 2. Graph the solution set of the second linear inequality. Page 109 of 123 Step 3. Graph the solution set for the system. 43. Consider the following nonlinear system of equations. Step 1. Determine the type and key parts of the graph of the first equation. Page 110 of 123 { 6𝑥 + 7𝑦 = 42 𝑥2 49 + 𝑦2 36 = 1 Answer: ____________________ Step 2. Determine the type and key parts of the graph of the second equation. 6𝑥 + 7𝑦 = 42 2 { 𝑥2 + 𝑦36 = 1 49 Answer: ____________________ Step 3. Find the real solution(s), if any, of the system by examining the graph. Verify the solutions algebraically. 6𝑥 + 7𝑦 = 42 2 { 𝑥2 + 𝑦36 = 1 49 Answer: __________ 44. Consider the following nonlinear system of equations. Step 1. Determine the type and key parts of the graph of the first equation. 𝑦 − 1 = 12(𝑥 + 3)2 { 𝑦 + 1 = (𝑥 + 3)2 Answer: ____________________ Step 2. Determine the type and key parts of the graph of the second equation. 𝑦 − 1 = 12(𝑥 + 3)2 { 𝑦 + 1 = (𝑥 + 3)2 Answer: ____________________ Step 3. Find the real solution(s), if any, of the system by examining the graph. Verify the solutions algebraically. 𝑦 − 1 = 12(𝑥 + 3)2 { 𝑦 + 1 = (𝑥 + 3)2 Answer: __________ Page 111 of 123 45. Solve the following nonlinear system algebraically. Be sure to check for non-real solutions. { 4𝑥 2 + 𝑦 2 = 80 4( 𝑥 + 3 )2 + 𝑦 2 = 20 Answer: __________ 46. Solve the following nonlinear system algebraically. Be sure to check for non-real solutions. { 𝑥 2 + 𝑦 2 = 20 4𝑥 2 − 5𝑦 2 = −64 Answer: __________ 47. The product of two positive integers is 130, and their sum is 23. What are the integers? Answer: _______________ _______________ X Help MAT 110.06 Fela S. X SUNG Acrobat Pro DC 02- Ⓒ 105 / 126 24. 25. 26. 27. Answer: A Evaluate the determinant of the matrix. Answer: Answer: Answer: A Evaluate the determinant of the matrix Answer: 4-12-2 A Evaluate the determinant of the matric A A- 8. P A- ac d Ba Given the following matrices, if possible, determine A +8+C. IN Possible". -63-83-63 P 6040 & fim Contest Cannab Q a do adae14 MCM.pd- Adobe Acrobat PDC2-6 Window Help x MAT 110.06 Felix S... x Q 37. 38. 39. 40 41. 126 Answer: VA Answer: Find the inverse of the following matris, if possible. Reduce all fractions to lowest terms Answer: A- & Find the inverse of the following matrix, if possible. Reduce all fractions to lowest terms 4-3 Pap 14 A- - Find the inverse of the following matrix, if possible. Reduce all fractions to lowest terms. Answer: Solve the system of two linear inequalities graphically >7
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33.
34.
35.
36.
2[x 2y 3r]- 4(x 3y 22)-12 64 201
A)x=
B) Not Possible
CA
Determine values of the variables that
If not, state “Not Possible”,
A) W-
B) Not Possible
3
I make the following equation true possible
Write the following system of equations as a single matrix equation
(4y + 13-8x
-171
Answer:
Write the following system of equations as a single matrix equation
y+ 5-
-2
8x +9y-5
2y91-12
Answer:
Write the following system of equations as a single matrix equation
6y
1+9y-14 .
0
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16.
17.
18.
19.
STA%
8) None
Step 2. Determine the value of a, if possible. If the element indicated is not in the
matrix, state “None”.
A)
8) None
Step 3. Determine the value of 043, if possible. If the element indicated is not in the
matrix, state “None”.
A)
{
Construct the augmented matrix that corresponds to the following system of equations
–
3x + 5
3(48-5x) + y -5 –
x- (6+)
42 – 3(x – 4y)
5x – y
&
4
6
-Sy
Answer:
Construct the augmented matrix that corresponds to the following intem of equations
-3(x-60)
free tha
Answer:
Fill in the blank by performing the indicated elementary row operation
-48, 1
Answer:
Use Gaussian elimination and back-substitution to solve the following te of
equations. If there is a solution, write your answer in the format (.)
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43.
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Step 3. Graph the solution set for the system.
Consider the following nonlinear system of equations
Step 1 Determine the type and key parts of the graph of the first equation
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