Question 1

Solve the system by any method, if possible. $x ^ { 2 } - 2 x = 7$

Accepted Answer

A)  $x = 1 \pm 2 \sqrt { 2 }$ 
B)  $16 i$ 
C)  $- 36 i$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system 
A)  $x = 1 \pm 2 \sqrt { 2 }$ 
B)  $16 i$ 
C)  $- 36 i$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system

Question 2

Solve the system. Give your answer as an ordered triple in the form of ( r, s, t ). 
$\left\{ \begin{array} { l } 
r - s + t = 8 \
r + 2 s - t = - 5 \
r + s - 3 t = - 6
\end{array} \right.$

Accepted Answer

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

Question 3

Refer to the illustration.  
 (a) How many ordered pairs satisfy the equation $5 x + y = 5$ ?
(b) How many ordered pairs satisfy the equation $\frac { 3 } { 4 } x - y = - 5$ ?
(c) How many ordered pairs satisfy both equations?

Accepted Answer

A)  (a) infinitely many (b) infinitely many (c) infinitely many 
B)  (a) infinitely many (b) infinitely many (c) one 
C)  (a) one (b) one (c) infinitely many 
D)  (a) one (b) one (c) one 
E)  (a) infinitely many (b) infinitely many (c) none 
A)  (a) infinitely many (b) infinitely many (c) infinitely many 
B)  (a) infinitely many (b) infinitely many (c) one 
C)  (a) one (b) one (c) infinitely many 
D)  (a) one (b) one (c) one 
E)  (a) infinitely many (b) infinitely many (c) none

Question 4

Solve the system. $\left\{ \begin{array} { l } 
x + y + z = 5 \
2 x + y - z = 5 \
2 x - 3 y + z = - 1
\end{array} \right.$

Accepted Answer

A)  $( - 3 , - 1,1 )$ 
B)  $( 2 , - 2 , - 1 )$ 
C)  $( 2,2,1 )$ 
D)  The equations are dependent. 
E)  The system is inconsistent. 
A)  $( - 3 , - 1,1 )$ 
B)  $( 2 , - 2 , - 1 )$ 
C)  $( 2,2,1 )$ 
D)  The equations are dependent. 
E)  The system is inconsistent.

Question 5

Solve the system by any method if possible. $\log _ { 5 } 3$

Accepted Answer

A)  $\frac { \log 3 } { \log 5 }$ 
B)  $\frac { \log 5 } { \log 3 }$ 
C)  $\frac { \ln 5 } { \ln 3 }$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system 
A)  $\frac { \log 3 } { \log 5 }$ 
B)  $\frac { \log 5 } { \log 3 }$ 
C)  $\frac { \ln 5 } { \ln 3 }$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system

Question 6

Which of the following ordered triples is a solution of the system $\left\{ \begin{array} { l } 
x - 2 y + 3 z = 21 \
3 x - 6 y - z = 13 \
5 x - 2 y + z = 19
\end{array} \right.$ ?

Accepted Answer

A)  $\left( 2 , - 2 , \frac { 1 } { 9 } \right)$ 
B)  $\left( 2 , - \frac { 13 } { 8 } , 2 \right)$ 
C)  $( 2 , - 11 , - 2 )$ 
D)  $( 2 , - 2,5 )$ 
A)  $\left( 2 , - 2 , \frac { 1 } { 9 } \right)$ 
B)  $\left( 2 , - \frac { 13 } { 8 } , 2 \right)$ 
C)  $( 2 , - 11 , - 2 )$ 
D)  $( 2 , - 2,5 )$

Question 7

A $2 \times 3$ matrix has _____ rows.

Accepted Answer

The answer of A $2 \times 3$ matrix has _____...

Question 8

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 
x + y + z = 8 \
x + 2 y + z = 10 \
x + y + 2 z = 11
\end{array} \right.$

Accepted Answer

The answer of Use matrices to solve the system of...

Question 9

Solve the system by graphing. $\left\{ \begin{array} { l } 
x + y = 0 \
y = 2 x - 9
\end{array} \right.$

Accepted Answer

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

Question 10

If a point lies on the graph of an equation, it is a solution of the equation, and the coordinates of the point _________ the equation.

Accepted Answer

The answer of If a point lies on the graph...

Question 11

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 
3 x + y = 11 \
x + 3 y = - 7
\end{array} \right.$

Accepted Answer

A)  (5,-4) 
B)  (6,-30 
C)  (-5,4) 
D)  no solution 
E)  infinitely many solutions 
A)  (5,-4) 
B)  (6,-30 
C)  (-5,4) 
D)  no solution 
E)  infinitely many solutions

Question 12

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 
0.02 a = 0.02 - 0.03 b - 0.01 c \
4 a + 6 b + 2 c - 5 = 0 \
a + c = 3 + 2 b
\end{array} \right.$

Accepted Answer

The answer of Solve the system. If a system is...

Question 13

The process of determining an equation whose graph contains given points is called curve _________,

Accepted Answer

The answer of The process of determining an equation whose...

Question 14

Solve the system. Give your answer as an ordered triple in the form of ( a, b, c ). 
$\left\{ \begin{array} { l } 
0.02 a = 0.02 - 0.03 b - 0.01 c \
4 a + 6 b + 2 c - 5 = 0 \
a + c = 3 + 2 b
\end{array} \right.$

Accepted Answer

A)  $( 2,0 , - 3 )$ 
B)  $( 2,0,3 )$ 
C)  $( - 2,0,3 )$ 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  $( 2,0 , - 3 )$ 
B)  $( 2,0,3 )$ 
C)  $( - 2,0,3 )$ 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 15

To solve $f \text { and } f ^ { - 1 }$ , we can __________ $( f \circ g ) ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$ for y in the second equation.

Accepted Answer

The answer of To solve \(f \text { and }...

Question 16

The receipts for one showing of a movie were $1,018 for an audience of 167 people. Children's tickets are $3, general admission is $8, and tickets for seniors are $4. If twice as many general admission tickets as children's tickets were purchased, how many of each type were sold?

Accepted Answer

50 children's ticket

Question 17

Solve the system by any method if possible. If the system is inconsistent or if the equations are dependent, so indicate. $\sqrt { - 2 } \sqrt { - 14 }$

Accepted Answer

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

Question 18

A long distance provider offers two plans. Plan 1 has a monthly fee of $10 plus $0.14 per minute. Plan 2 has a monthly fee of $16 plus $0.12 per minute. For what number of minutes will the cost of the plans be the same?
 ______ minutes

Accepted Answer

The answer of A long distance provider offers two plans....

Question 19

Solve the system by substitution, if possible. $\log x + \log ( x - 15 ) = 2$

Accepted Answer

A)  (8, 3) 
B)  $\left\{ \frac { 500 } { 33 } \right\}$ 
C)  (3, 8) 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system 
A)  (8, 3) 
B)  $\left\{ \frac { 500 } { 33 } \right\}$ 
C)  (3, 8) 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system

Question 20

A hotel has rooms with two double beds, two queen-size beds, and one king-size bed. The room with two double beds rents for $87; the room with two queen-size beds rents for $93, and the room with a king-size bed rents for $108. The number of rooms with two queen-size beds is five more than twice the number of rooms with two double beds. The number of rooms with a king-size bed is five less than the number of rooms with two double beds. If all 140 rooms are rented, the total revenue is $13,260. Find the number of rooms for each type.

Accepted Answer

35 rooms with double

Solve the system by any method, if possible. $x ^ { 2 } - 2 x = 7$

Solve the system. Give your answer as an ordered triple in the form of ( r, s, t ). $\left\{ \begin{array} { l } r - s + t = 8 \\r + 2 s - t = - 5 \\r + s - 3 t = - 6\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } x + y + z = 5 \\2 x + y - z = 5 \\2 x - 3 y + z = - 1\end{array} \right.$

Solve the system by any method if possible. $\log _ { 5 } 3$

Which of the following ordered triples is a solution of the system $\left\{ \begin{array} { l } x - 2 y + 3 z = 21 \\3 x - 6 y - z = 13 \\5 x - 2 y + z = 19\end{array} \right.$ ?

A $2 \times 3$ matrix has _____ rows.

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } x + y + z = 8 \\x + 2 y + z = 10 \\x + y + 2 z = 11\end{array} \right.$

Solve the system by graphing. $\left\{ \begin{array} { l } x + y = 0 \\y = 2 x - 9\end{array} \right.$

If a point lies on the graph of an equation, it is a solution of the equation, and the coordinates of the point _________ the equation.

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 3 x + y = 11 \\x + 3 y = - 7\end{array} \right.$

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 0.02 a = 0.02 - 0.03 b - 0.01 c \\4 a + 6 b + 2 c - 5 = 0 \\a + c = 3 + 2 b\end{array} \right.$

The process of determining an equation whose graph contains given points is called curve _________,

Solve the system. Give your answer as an ordered triple in the form of ( a, b, c ). $\left\{ \begin{array} { l } 0.02 a = 0.02 - 0.03 b - 0.01 c \\4 a + 6 b + 2 c - 5 = 0 \\a + c = 3 + 2 b\end{array} \right.$

To solve $f \text { and } f ^ { - 1 }$ , we can __________ $( f \circ g ) ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$ for y in the second equation.

The receipts for one showing of a movie were $1,018 for an audience of 167 people. Children's tickets are $3, general admission is $8, and tickets for seniors are $4. If twice as many general admission tickets as children's tickets were purchased, how many of each type were sold?

Solve the system by any method if possible. If the system is inconsistent or if the equations are dependent, so indicate. $\sqrt { - 2 } \sqrt { - 14 }$

A long distance provider offers two plans. Plan 1 has a monthly fee of $10 plus $0.14 per minute. Plan 2 has a monthly fee of $16 plus $0.12 per minute. For what number of minutes will the cost of the plans be the same? ______ minutes

Solve the system by substitution, if possible. $\log x + \log ( x - 15 ) = 2$

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 the system by any method, if possible. x2−2x=7x ^ { 2 } - 2 x = 7x2−2x=7

Solve the system. Give your answer as an ordered triple in the form of ( r, s, t ). {r−s+t=8r+2s−t=−5r+s−3t=−6\left\{ \begin{array} { l } r - s + t = 8 \\r + 2 s - t = - 5 \\r + s - 3 t = - 6\end{array} \right.⎩⎨⎧​r−s+t=8r+2s−t=−5r+s−3t=−6​

Refer to the illustration. (a) How many ordered pairs satisfy the equation 5x+y=55 x + y = 55x+y=5 ? (b) How many ordered pairs satisfy the equation 34x−y=−5\frac { 3 } { 4 } x - y = - 543​x−y=−5 ? (c) How many ordered pairs satisfy both equations?

Solve the system. {x+y+z=52x+y−z=52x−3y+z=−1\left\{ \begin{array} { l } x + y + z = 5 \\2 x + y - z = 5 \\2 x - 3 y + z = - 1\end{array} \right.⎩⎨⎧​x+y+z=52x+y−z=52x−3y+z=−1​

Solve the system by any method if possible. log⁡53\log _ { 5 } 3log5​3

Which of the following ordered triples is a solution of the system {x−2y+3z=213x−6y−z=135x−2y+z=19\left\{ \begin{array} { l } x - 2 y + 3 z = 21 \\3 x - 6 y - z = 13 \\5 x - 2 y + z = 19\end{array} \right.⎩⎨⎧​x−2y+3z=213x−6y−z=135x−2y+z=19​ ?

A 2×32 \times 32×3 matrix has _____ rows.

Solve the system by graphing. {x+y=0y=2x−9\left\{ \begin{array} { l } x + y = 0 \\y = 2 x - 9\end{array} \right.{x+y=0y=2x−9​

If a point lies on the graph of an equation, it is a solution of the equation, and the coordinates of the point _________ the equation.

Use matrices to solve the system of equations. {3x+y=11x+3y=−7\left\{ \begin{array} { l } 3 x + y = 11 \\x + 3 y = - 7\end{array} \right.{3x+y=11x+3y=−7​

The process of determining an equation whose graph contains given points is called curve _________,

To solve f and f−1f \text { and } f ^ { - 1 }f and f−1 , we can __________ (f∘g)(x)=x3+9x2+27x+27( f \circ g ) ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27(f∘g)(x)=x3+9x2+27x+27 for y in the second equation.

The receipts for one showing of a movie were $1,018 for an audience of 167 people. Children's tickets are $3, general admission is $8, and tickets for seniors are $4. If twice as many general admission tickets as children's tickets were purchased, how many of each type were sold?

Solve the system by any method if possible. If the system is inconsistent or if the equations are dependent, so indicate. −2−14\sqrt { - 2 } \sqrt { - 14 }−2​−14​

A long distance provider offers two plans. Plan 1 has a monthly fee of $10 plus $0.14 per minute. Plan 2 has a monthly fee of $16 plus $0.12 per minute. For what number of minutes will the cost of the plans be the same? ______ minutes

Solve the system by substitution, if possible. log⁡x+log⁡(x−15)=2\log x + \log ( x - 15 ) = 2logx+log(x−15)=2

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 the system by any method, if possible. $x ^ { 2 } - 2 x = 7$

Solve the system. Give your answer as an ordered triple in the form of ( r, s, t ). $\left\{ \begin{array} { l } r - s + t = 8 \\r + 2 s - t = - 5 \\r + s - 3 t = - 6\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } x + y + z = 5 \\2 x + y - z = 5 \\2 x - 3 y + z = - 1\end{array} \right.$

Solve the system by any method if possible. $\log _ { 5 } 3$

Which of the following ordered triples is a solution of the system $\left\{ \begin{array} { l } x - 2 y + 3 z = 21 \\3 x - 6 y - z = 13 \\5 x - 2 y + z = 19\end{array} \right.$ ?

A $2 \times 3$ matrix has _____ rows.

Solve the system by graphing. $\left\{ \begin{array} { l } x + y = 0 \\y = 2 x - 9\end{array} \right.$

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 3 x + y = 11 \\x + 3 y = - 7\end{array} \right.$

To solve $f \text { and } f ^ { - 1 }$ , we can __________ $( f \circ g ) ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$ for y in the second equation.

Solve the system by any method if possible. If the system is inconsistent or if the equations are dependent, so indicate. $\sqrt { - 2 } \sqrt { - 14 }$

Solve the system by substitution, if possible. $\log x + \log ( x - 15 ) = 2$