Question 1

Solve using substitution: $\left\{ \begin{array} { l } 
x - 8 z = - 8 \
7 x + y + 8 z = 5 \
y + 4 z = 1
\end{array} \right.$

Accepted Answer

The answer of Solve using substitution: \(\left\{ \begin{array} { l...

Question 2

Solve the system by any method, if possible. If the system is inconsistent or if the equations are dependent, so indicate. $a + b i$

Accepted Answer

The answer of Solve the system by any method, if...

Question 3

Solve the system by graphing. $\left\{ \begin{array} { l } 
x = 2 - 2 y \
2 x + 4 y = 4
\end{array} \right.$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

For the following augmented matrix, give the system of equations it represents. $\left[ \begin{array} { l l | l } 
1 & 7 & 5 \
0 & 1 & 3
\end{array} \right]$

Accepted Answer

The answer of For the following augmented matrix, give the...

Question 5

Solve the system by graphing. $\left\{ \begin{array} { l } 
y = - 4 \
y = \frac { 13 } { 4 } x - \frac { 3 } { 4 }
\end{array} \right.$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. The annual income from these investments is $1,060. How much was invested at 10%?
 $__________ How much was invested at 12%?
 $__________

Accepted Answer

The answer of Part of $9,000 was invested by an...

Question 7

Consider the matrix $\left[ \begin{array} { c c : c } 
1 & - 4 & 8 \
2 & 8 & 8
\end{array} \right]$ . What elementary row operation was performed to obtain the matrix $\left[ \begin{array} { c c : c } 
1 & - 4 & 8 \
0 & 16 & - 8
\end{array} \right]$ ?

Accepted Answer

A)  $- 2 R _ { 1 } + R _ { 2 }$ 
B)  $2 R _ { 1 } + R _ { 2 }$ 
C)  $- 2 R _ { 2 } + R _ { 1 }$ 
D)  $2 R _ { 2 } + R _ { 1 }$ 
A)  $- 2 R _ { 1 } + R _ { 2 }$ 
B)  $2 R _ { 1 } + R _ { 2 }$ 
C)  $- 2 R _ { 2 } + R _ { 1 }$ 
D)  $2 R _ { 2 } + R _ { 1 }$

Question 8

Evaluate the determinant. $\left| \begin{array} { r r } 
- 9 & 6 \
5 & - 2
\end{array} \right|$

Accepted Answer

A)  -8 
B)  -14 
C)  -15 
D)  -12 
E)  -11 
A)  -8 
B)  -14 
C)  -15 
D)  -12 
E)  -11

Question 9

Consider the augmented matrix $\left[ \begin{array} { l l : l } 
1 & - 1 & 2 \
8 & - 6 & 4
\end{array} \right]$ . Which of the following matrices shows the elementary row operation $- 8 R _ { 1 } + R _ { 2 }$ ?

Accepted Answer

A)  $\left[ \begin{array} { c c : c } 
1 & - 1 & 2 \
0 & - 14 & - 12
\end{array} \right]$ 
B)  $\left[ \begin{array} { l l : l } 
1 & - 1 & 2 \
0 & - 2 & 20
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c : c } 
1 & - 1 & 2 \
0 & 2 & - 12
\end{array} \right]$ 
D)  none of these 
A)  $\left[ \begin{array} { c c : c } 
1 & - 1 & 2 \
0 & - 14 & - 12
\end{array} \right]$ 
B)  $\left[ \begin{array} { l l : l } 
1 & - 1 & 2 \
0 & - 2 & 20
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c : c } 
1 & - 1 & 2 \
0 & 2 & - 12
\end{array} \right]$ 
D)  none of these

Question 10

Find the equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola shown in the illustration.

Accepted Answer

The answer of Find the equation of the form \(y...

Question 11

Solve the system using the substitution method, if possible. If the system is inconsistent or if the equations are dependent , so indicate. $i$

Accepted Answer

The answer of Solve the system using the substitution method,...

Question 12

The __________ of $\left| \begin{array} { l l l } 
a _ { 1 } & b _ { 1 } & c _ { 1 } \
a _ { 2 } & b _ { 2 } & c _ { 2 } \
a _ { 3 } & b _ { 3 } & c _ { 3 }
\end{array} \right|$ in $\left| \begin{array} { l l } 
a _ { 1 } & c _ { 1 } \
a _ { 3 } & c _ { 3 }
\end{array} \right|$ is $\left| \begin{array} { l l } 
a _ { 1 } & c _ { 1 } \
a _ { 3 } & c _ { 3 }
\end{array} \right|$ .

Accepted Answer

A)  matrix 
B)  minor 
C)  value 
D)  diagonal 
E)  determinant 
A)  matrix 
B)  minor 
C)  value 
D)  diagonal 
E)  determinant

Question 13

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 
x - y = 4 \
2 x + y = 5
\end{array} \right.$

Accepted Answer

The answer of Use Cramer s rule to solve the...

Question 14

A(n) __________ is a rectangular array of numbers written within brackets.

Accepted Answer

The answer of A(n) __________ is a rectangular array of...

Question 15

When a system of equations has at least one solution, it is called a(n) __________ system. If a system has no solutions, it is called a(n) __________ system.

Accepted Answer

The answer of When a system of equations has at...

Question 16

Solve the system by graphing. $\left\{ \begin{array} { l } 
x = 2 \
y = - \frac { 1 } { 2 } x + 3
\end{array} \right.$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Solve the following system by graphing. Write the solution as an ordered pair. If a system is inconsistent or is the equations are independent, so state. $\left\{ \begin{array} { l } 
x + y = 3 \
x - y = 1
\end{array} \right.$

Accepted Answer

The answer of Solve the following system by graphing. Write...

Question 18

Find the value of b that makes the following system inconsistent. $\sqrt { - 4 } \cdot \sqrt { - 100 }$

Accepted Answer

A)  b = 36 
B)  b = - 36 
C)  $20 i$ 
D)  $20$ 
A)  b = 36 
B)  b = - 36 
C)  $20 i$ 
D)  $20$

Question 19

Solve the system. $\left\{ \begin{array} { l } 
x + y + z = 4 \
x - y + z = 0 \
x - y - z = 6
\end{array} \right.$

Accepted Answer

A)  $( 4,2 , - 3 )$ 
B)  $( 5,2 , - 3 )$ 
C)  $( - 5,2 , - 3 )$ 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  $( 4,2 , - 3 )$ 
B)  $( 5,2 , - 3 )$ 
C)  $( - 5,2 , - 3 )$ 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 20

Without graphing, how can you tell that the graphs of $y = 3 x - 7 \text { and } y = 3 x + 2$ do no intersect?

Accepted Answer

Since the slopes are the same

Solve using substitution: $\left\{ \begin{array} { l } x - 8 z = - 8 \\7 x + y + 8 z = 5 \\y + 4 z = 1\end{array} \right.$

Solve the system by any method, if possible. If the system is inconsistent or if the equations are dependent, so indicate. $a + b i$

Solve the system by graphing. $\left\{ \begin{array} { l } x = 2 - 2 y \\2 x + 4 y = 4\end{array} \right.$

For the following augmented matrix, give the system of equations it represents. $\left[ \begin{array} { l l | l } 1 & 7 & 5 \\0 & 1 & 3\end{array} \right]$

Solve the system by graphing. $\left\{ \begin{array} { l } y = - 4 \\y = \frac { 13 } { 4 } x - \frac { 3 } { 4 }\end{array} \right.$

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. The annual income from these investments is $1,060. How much was invested at 10%? $ How much was invested at 12%? $

Consider the matrix $\left[ \begin{array} { c c : c } 1 & - 4 & 8 \\2 & 8 & 8\end{array} \right]$ . What elementary row operation was performed to obtain the matrix $\left[ \begin{array} { c c : c } 1 & - 4 & 8 \\0 & 16 & - 8\end{array} \right]$ ?

Evaluate the determinant. $\left| \begin{array} { r r } - 9 & 6 \\5 & - 2\end{array} \right|$

Consider the augmented matrix $\left[ \begin{array} { l l : l } 1 & - 1 & 2 \\8 & - 6 & 4\end{array} \right]$ . Which of the following matrices shows the elementary row operation $- 8 R _ { 1 } + R _ { 2 }$ ?

Find the equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola shown in the illustration. $Find the equation of the form y = a x ^ { 2 } + b x + c for the parabola shown in the illustration.$

Solve the system using the substitution method, if possible. If the system is inconsistent or if the equations are dependent , so indicate. $i$

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } x - y = 4 \\2 x + y = 5\end{array} \right.$

A(n) __________ is a rectangular array of numbers written within brackets.

When a system of equations has at least one solution, it is called a(n) system. If a system has no solutions, it is called a(n) system.

Solve the system by graphing. $\left\{ \begin{array} { l } x = 2 \\y = - \frac { 1 } { 2 } x + 3\end{array} \right.$

Find the value of b that makes the following system inconsistent. $\sqrt { - 4 } \cdot \sqrt { - 100 }$

Solve the system. $\left\{ \begin{array} { l } x + y + z = 4 \\x - y + z = 0 \\x - y - z = 6\end{array} \right.$

Without graphing, how can you tell that the graphs of $y = 3 x - 7 \text { and } y = 3 x + 2$ do no intersect?

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 3: Systems of Equations

Solve using substitution: {x−8z=−87x+y+8z=5y+4z=1\left\{ \begin{array} { l } x - 8 z = - 8 \\7 x + y + 8 z = 5 \\y + 4 z = 1\end{array} \right.⎩⎨⎧​x−8z=−87x+y+8z=5y+4z=1​

Solve the system by any method, if possible. If the system is inconsistent or if the equations are dependent, so indicate. a+bia + b ia+bi

Solve the system by graphing. {x=2−2y2x+4y=4\left\{ \begin{array} { l } x = 2 - 2 y \\2 x + 4 y = 4\end{array} \right.{x=2−2y2x+4y=4​

For the following augmented matrix, give the system of equations it represents. [175013]\left[ \begin{array} { l l | l } 1 & 7 & 5 \\0 & 1 & 3\end{array} \right][10​71​53​]

Solve the system by graphing. {y=−4y=134x−34\left\{ \begin{array} { l } y = - 4 \\y = \frac { 13 } { 4 } x - \frac { 3 } { 4 }\end{array} \right.{y=−4y=413​x−43​​

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. The annual income from these investments is $1,060. How much was invested at 10%? $__________ How much was invested at 12%? $__________

Evaluate the determinant. ∣−965−2∣\left| \begin{array} { r r } - 9 & 6 \\5 & - 2\end{array} \right|​−95​6−2​​

Consider the augmented matrix [1−128−64]\left[ \begin{array} { l l : l } 1 & - 1 & 2 \\8 & - 6 & 4\end{array} \right][18​−1−6​24​] . Which of the following matrices shows the elementary row operation −8R1+R2- 8 R _ { 1 } + R _ { 2 }−8R1​+R2​ ?

Find the equation of the form y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c for the parabola shown in the illustration.

Solve the system using the substitution method, if possible. If the system is inconsistent or if the equations are dependent , so indicate. iii

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. {x−y=42x+y=5\left\{ \begin{array} { l } x - y = 4 \\2 x + y = 5\end{array} \right.{x−y=42x+y=5​

A(n) __________ is a rectangular array of numbers written within brackets.

When a system of equations has at least one solution, it is called a(n) __________ system. If a system has no solutions, it is called a(n) __________ system.

Solve the system by graphing. {x=2y=−12x+3\left\{ \begin{array} { l } x = 2 \\y = - \frac { 1 } { 2 } x + 3\end{array} \right.{x=2y=−21​x+3​

Solve the following system by graphing. Write the solution as an ordered pair. If a system is inconsistent or is the equations are independent, so state. {x+y=3x−y=1\left\{ \begin{array} { l } x + y = 3 \\x - y = 1\end{array} \right.{x+y=3x−y=1​

Find the value of b that makes the following system inconsistent. −4⋅−100\sqrt { - 4 } \cdot \sqrt { - 100 }−4​⋅−100​

Solve the system. {x+y+z=4x−y+z=0x−y−z=6\left\{ \begin{array} { l } x + y + z = 4 \\x - y + z = 0 \\x - y - z = 6\end{array} \right.⎩⎨⎧​x+y+z=4x−y+z=0x−y−z=6​

Without graphing, how can you tell that the graphs of y=3x−7 and y=3x+2y = 3 x - 7 \text { and } y = 3 x + 2y=3x−7 and y=3x+2 do no intersect?

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Solve using substitution: $\left\{ \begin{array} { l } x - 8 z = - 8 \\7 x + y + 8 z = 5 \\y + 4 z = 1\end{array} \right.$

Solve the system by any method, if possible. If the system is inconsistent or if the equations are dependent, so indicate. $a + b i$

Solve the system by graphing. $\left\{ \begin{array} { l } x = 2 - 2 y \\2 x + 4 y = 4\end{array} \right.$

For the following augmented matrix, give the system of equations it represents. $\left[ \begin{array} { l l | l } 1 & 7 & 5 \\0 & 1 & 3\end{array} \right]$

Solve the system by graphing. $\left\{ \begin{array} { l } y = - 4 \\y = \frac { 13 } { 4 } x - \frac { 3 } { 4 }\end{array} \right.$

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. The annual income from these investments is $1,060. How much was invested at 10%? $ How much was invested at 12%? $

Evaluate the determinant. $\left| \begin{array} { r r } - 9 & 6 \\5 & - 2\end{array} \right|$

Consider the augmented matrix $\left[ \begin{array} { l l : l } 1 & - 1 & 2 \\8 & - 6 & 4\end{array} \right]$ . Which of the following matrices shows the elementary row operation $- 8 R _ { 1 } + R _ { 2 }$ ?

Find the equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola shown in the illustration. $Find the equation of the form y = a x ^ { 2 } + b x + c for the parabola shown in the illustration.$

Solve the system using the substitution method, if possible. If the system is inconsistent or if the equations are dependent , so indicate. $i$

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } x - y = 4 \\2 x + y = 5\end{array} \right.$

When a system of equations has at least one solution, it is called a(n) system. If a system has no solutions, it is called a(n) system.

Solve the system by graphing. $\left\{ \begin{array} { l } x = 2 \\y = - \frac { 1 } { 2 } x + 3\end{array} \right.$

Find the value of b that makes the following system inconsistent. $\sqrt { - 4 } \cdot \sqrt { - 100 }$

Solve the system. $\left\{ \begin{array} { l } x + y + z = 4 \\x - y + z = 0 \\x - y - z = 6\end{array} \right.$

Without graphing, how can you tell that the graphs of $y = 3 x - 7 \text { and } y = 3 x + 2$ do no intersect?