Question 1

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x y = 20 \
x + y = 9
\end{array} \right.$$

Accepted Answer

A)  $x = 6 , y = 3 ; x = 3 , y = 6$ 
B)  $x = 10 , y = 2 ; x = 2 , y = 10$ 
C)  $x = 5 , y = 4 ; x = 4 , y = 5$ 
D)  $x = 20 , y = 1 ; x = 1 , y = 20$ 
A)  $x = 6 , y = 3 ; x = 3 , y = 6$ 
B)  $x = 10 , y = 2 ; x = 2 , y = 10$ 
C)  $x = 5 , y = 4 ; x = 4 , y = 5$ 
D)  $x = 20 , y = 1 ; x = 1 , y = 20$

Question 2

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
y = - x ^ { 2 } + 3 \
x ^ { 2 } + y ^ { 2 } = 5
\end{array} \right.$$

Accepted Answer

A)  $x = 1 , y = 4 ; x = 4 , y = 19$ 
B)  $x = 1 , y = 2 ; x = - 1 , y = 2$ 
C)  $x = 2 , y = - 1 ; x = 1 , y = 2 ; x = - 1 , y = 2 ; x = - 2 , y = - 1$ 
D)  $x = 2 , y = - 1 ; x = - 2 , y = - 1$ 
A)  $x = 1 , y = 4 ; x = 4 , y = 19$ 
B)  $x = 1 , y = 2 ; x = - 1 , y = 2$ 
C)  $x = 2 , y = - 1 ; x = 1 , y = 2 ; x = - 1 , y = 2 ; x = - 2 , y = - 1$ 
D)  $x = 2 , y = - 1 ; x = - 2 , y = - 1$

Question 3

Choose the one alternative that best completes the statement or answers the question.
-Let $A = \left[ \begin{array} { r r r } - 2 & - 9 & - 8 \ 6 & - 9 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 6 & - 4 & - 5 \ 8 & - 4 & - 3 \ - 3 & - 7 & 3 \end{array} \right]$. Find $A B$.

Accepted Answer

A)  $\left[ \begin{array} { r r } - 60 & - 33 \ 100 & 19 \ 13 & - 6 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 12 & 36 & 40 \ 48 & 36 & 3 \ - 18 & 63 & - 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 2 & - 9 & - 8 \ 6 & - 9 & - 1 \ 6 & - 9 & - 1 \ 8 & - 4 & - 3 \ - 3 & - 3 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 60 & 100 & 13 \ - 33 & 19 & - 6 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } - 60 & - 33 \ 100 & 19 \ 13 & - 6 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 12 & 36 & 40 \ 48 & 36 & 3 \ - 18 & 63 & - 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 2 & - 9 & - 8 \ 6 & - 9 & - 1 \ 6 & - 9 & - 1 \ 8 & - 4 & - 3 \ - 3 & - 3 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 60 & 100 & 13 \ - 33 & 19 & - 6 \end{array} \right]$

Question 4

2x + 3y ≥6
-$$\begin{array} { l } 
x ^ { 2 } + y \leq 1 \
x ^ { 2 } - y \leq 3
\end{array}$$

Accepted Answer

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

Question 5

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x y - x ^ { 2 } = - 20 \
x - 2 y = 3
\end{array} \right.$$

Accepted Answer

A)  $x = - 5 , y = - 1 ; x = 8 , y = \frac { 11 } { 2 }$ 
B)  $x = - 5 , y = - 1 ; x = \frac { 11 } { 2 } , y = 8$ 
C)  $x = 5 , y = 1 ; x = - \frac { 11 } { 2 } , y = - 8$ 
D)  $x = 5 , y = 1 ; x = - 8 , y = - \frac { 11 } { 2 }$ 
A)  $x = - 5 , y = - 1 ; x = 8 , y = \frac { 11 } { 2 }$ 
B)  $x = - 5 , y = - 1 ; x = \frac { 11 } { 2 } , y = 8$ 
C)  $x = 5 , y = 1 ; x = - \frac { 11 } { 2 } , y = - 8$ 
D)  $x = 5 , y = 1 ; x = - 8 , y = - \frac { 11 } { 2 }$

Question 6

Write the augmented matrix for the system.
-$$\left\{ \begin{aligned}
4 x + 9 y + 2 z & = 30 \
- 2 x + 6 y + 2 z & = 0 \
9 x + 6 y + 5 z & = 38
\end{aligned} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { r r | r } 4 & 9 & 2 \ - 2 & 6 & 2 \ 9 & 6 & 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r | r } 30 & 2 & 9 & 4 \ 0 & 2 & 6 & - 2 \ 38 & 5 & 6 & 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r | r } 4 & 9 & 2 & 30 \ - 2 & 6 & 2 & 0 \ 9 & 6 & 5 & 38 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r | r } 4 & - 2 & 9 & 30 \ 9 & 6 & 6 & 0 \ 2 & 2 & 5 & 38 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r | r } 4 & 9 & 2 \ - 2 & 6 & 2 \ 9 & 6 & 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r | r } 30 & 2 & 9 & 4 \ 0 & 2 & 6 & - 2 \ 38 & 5 & 6 & 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r | r } 4 & 9 & 2 & 30 \ - 2 & 6 & 2 & 0 \ 9 & 6 & 5 & 38 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r | r } 4 & - 2 & 9 & 30 \ 9 & 6 & 6 & 0 \ 2 & 2 & 5 & 38 \end{array} \right]$

Question 7

Solve the system of equations.
-$$\left\{ \begin{array} { l } 
x - y + 3 z = - 4 \
3 x + z = 0 \
- x + y - 3 z = 16
\end{array} \right.$$

Accepted Answer

A)  $x = 4 , y = 2 , z = 0$ 
B)  inconsistent (no solution) 
C)  $x = 0 , y = 0 , z = 2$ 
D)  $x = 0 , y = 2 , z = 0$ 
A)  $x = 4 , y = 2 , z = 0$ 
B)  inconsistent (no solution) 
C)  $x = 0 , y = 0 , z = 2$ 
D)  $x = 0 , y = 2 , z = 0$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Find the value of the determinant.
-$$\left| \begin{array} { r r } 
12 & - 7 \
- 4 & 3
\end{array} \right|$$

Accepted Answer

A)  4 
B)  8 
C)  64 
D)  $- 8$ 
A)  4 
B)  8 
C)  64 
D)  $- 8$

Question 9

Write the word or phrase that best completes each statement or answers the question.
-$$\frac { 7 x ^ { 3 } - 2 } { x ^ { 2 } ( x + 1 ) ^ { 3 } }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 10

Write the word or phrase that best completes each statement or answers the question.
Solve for x.
-$$\left| \begin{array} { l l } 
8 & x \
2 & 5
\end{array} \right| = 32$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 11

Write the word or phrase that best completes each statement or answers the question.
Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$\begin{aligned}
- 3 x ^ { 2 } - y ^ { 2 } & = 4 \
- 10 x ^ { 2 } + 3 y ^ { 2 } & = 64
\end{aligned}$

Accepted Answer

Either method may be used. Elimination m

Question 12

Verify that the values of the variables listed are solutions of the system of equations.
-$$\begin{array} { l } 
\left\{ \begin{array} { l } 
4 x + y = 13 \
2 x + 4 y = 24
\end{array} \right. \
\end{array}$$
x = 2 , y = 5

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 13

Solve the system using the inverse method.
-$$\left\{ \begin{array} { r } 
2 x + 4 y - 5 z = - 8 \
x + 5 y + 2 z = - 1 \
3 x + 3 y + 3 z = 15
\end{array} \right.$$

Accepted Answer

A)  $x = 5 , y = 2 , z = - 2$ 
B)  $x = - 5 , y = - 2 , z = - 2$ 
C)  $x = 2 , y = 5 , z = 2$ 
D)  $x = 5 , y = - 2 , z = 2$ 
A)  $x = 5 , y = 2 , z = - 2$ 
B)  $x = - 5 , y = - 2 , z = - 2$ 
C)  $x = 2 , y = 5 , z = 2$ 
D)  $x = 5 , y = - 2 , z = 2$

Question 14

Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l } 
- 4 x - 6 y - 8 z = - 84 \
- 4 x + 4 y - 3 z = 11 \
- 9 x - 5 y - 9 z = - 94
\end{array} \right.$$

Accepted Answer

A)  $x = 3 , y = 8 , z = 3$ 
B)  $x = 4 , y = 6 , z = 3$ 
C)  $x = 8 , y = 3 , z = 8$ 
D)  $x = 3 , y = - 8 , z = - 3$ 
A)  $x = 3 , y = 8 , z = 3$ 
B)  $x = 4 , y = 6 , z = 3$ 
C)  $x = 8 , y = 3 , z = 8$ 
D)  $x = 3 , y = - 8 , z = - 3$

Question 15

Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{aligned}
8 x - 3 z & = 29 \
2 x + 9 y + 5 z & = 104 \
2 x - 9 y & = - 31
\end{aligned} \right.$$

Accepted Answer

A)  $x = 8 , y = 3 , z = 9$ 
B)  $x = 7 , y = 5 , z = 9$ 
C)  $x = 7 , y = - 5 , z = - 9$ 
D)  $x = 5 , y = 9 , z = 5$ 
A)  $x = 8 , y = 3 , z = 9$ 
B)  $x = 7 , y = 5 , z = 9$ 
C)  $x = 7 , y = - 5 , z = - 9$ 
D)  $x = 5 , y = 9 , z = 5$

Question 16

Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l } 
9 x - 2 y - z = 64 \
x - 3 y - 3 z = - 27 \
- 6 x + y + z = - 42
\end{array} \right.$$

Accepted Answer

A)  $x = 10 , y = 3 , z = 7$ 
B)  $x = 9 , y = - 5 , z = - 7$ 
C)  $x = 5 , y = 7 , z = 5$ 
D)  $x = 9 , y = 5 , z = 7$ 
A)  $x = 10 , y = 3 , z = 7$ 
B)  $x = 9 , y = - 5 , z = - 7$ 
C)  $x = 5 , y = 7 , z = 5$ 
D)  $x = 9 , y = 5 , z = 7$

Question 17

2x + 3y ≥6
-$\left\{\begin{array}{l}
-x+2 y \leq-6 \
3 x+2 y>-18
\end{array}\right.$

Accepted Answer

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

Question 18

Write the word or phrase that best completes each statement or answers the question.
Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\left\{ \begin{array} { r } 
x ^ { 3 } + y ^ { 2 } = 2 \
x ^ { 2 } y = 4
\end{array} \right.$$

Accepted Answer

A)  $x = - 1.37 , y = 2.14$ 
B)  $x = 2.14 , y = - 1.37$ 
C)  $x = 2.14 , y = 1.37$ 
D)  $x = 1.37 , y = 2.14$ 
A)  $x = - 1.37 , y = 2.14$ 
B)  $x = 2.14 , y = - 1.37$ 
C)  $x = 2.14 , y = 1.37$ 
D)  $x = 1.37 , y = 2.14$

Question 19

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the
systems of equations. Are the points of intersection solutions to the system of equations (Y/N)?
-

$$\begin{array} { l } 
x ^ { 2 } = y - 1 \
y = - 3 x + 11
\end{array}$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 20

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 61 \
x - y = 1
\end{array} \right.$$

Accepted Answer

A)  $x = 4 , y = 5 ; x = 5 , y = 4$ 
B)  $x = 4 , y = - 5 ; x = 5 , y = - 4$ 
C)  $x = - 4 , y = - 5 ; x = 5 , y = 4$ 
D)  $x = - 4 , y = 5 ; x = - 5 , y = 4$ 
A)  $x = 4 , y = 5 ; x = 5 , y = 4$ 
B)  $x = 4 , y = - 5 ; x = 5 , y = - 4$ 
C)  $x = - 4 , y = - 5 ; x = 5 , y = 4$ 
D)  $x = - 4 , y = 5 ; x = - 5 , y = 4$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x y = 20 \\x + y = 9\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } y = - x ^ { 2 } + 3 \\x ^ { 2 } + y ^ { 2 } = 5\end{array} \right.$

2x + 3y ≥6 - +y\leq1 -y\leq3 $2x + 3y ≥6 - \begin{array} { l } x ^ { 2 } + y \leq 1 \\ x ^ { 2 } - y \leq 3 \end{array}$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x y - x ^ { 2 } = - 20 \\x - 2 y = 3\end{array} \right.$

Write the augmented matrix for the system. - $\left\{ \begin{aligned}4 x + 9 y + 2 z & = 30 \\- 2 x + 6 y + 2 z & = 0 \\9 x + 6 y + 5 z & = 38\end{aligned} \right.$

Solve the system of equations. - $\left\{ \begin{array} { l } x - y + 3 z = - 4 \\3 x + z = 0 \\- x + y - 3 z = 16\end{array} \right.$

Choose the one alternative that best completes the statement or answers the question. Find the value of the determinant. - $\left| \begin{array} { r r } 12 & - 7 \\- 4 & 3\end{array} \right|$

Write the word or phrase that best completes each statement or answers the question. - $\frac { 7 x ^ { 3 } - 2 } { x ^ { 2 } ( x + 1 ) ^ { 3 } }$

Write the word or phrase that best completes each statement or answers the question. Solve for x. - $\left| \begin{array} { l l } 8 & x \\2 & 5\end{array} \right| = 32$

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. - -3- =4 -10+3 =64

Verify that the values of the variables listed are solutions of the system of equations. - 4x+y=13 2x+4y=24 x = 2 , y = 5

Solve the system using the inverse method. - $\left\{ \begin{array} { r } 2 x + 4 y - 5 z = - 8 \\x + 5 y + 2 z = - 1 \\3 x + 3 y + 3 z = 15\end{array} \right.$

Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { l } - 4 x - 6 y - 8 z = - 84 \\- 4 x + 4 y - 3 z = 11 \\- 9 x - 5 y - 9 z = - 94\end{array} \right.$

Use Cramer's rule to solve the linear system. - $\left\{ \begin{aligned}8 x - 3 z & = 29 \\2 x + 9 y + 5 z & = 104 \\2 x - 9 y & = - 31\end{aligned} \right.$

Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { l } 9 x - 2 y - z = 64 \\x - 3 y - 3 z = - 27 \\- 6 x + y + z = - 42\end{array} \right.$

2x + 3y ≥6 - $\left\{\begin{array}{l}-x+2 y \leq-6 \\3 x+2 y>-18\end{array}\right.$ $2x + 3y ≥6 - \left\{\begin{array}{l} -x+2 y \leq-6 \\ 3 x+2 y>-18 \end{array}\right.$

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. - $\left\{ \begin{array} { r } x ^ { 3 } + y ^ { 2 } = 2 \\x ^ { 2 } y = 4\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x - y = 1\end{array} \right.$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

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Exam 10: Systems of Equations and Inequalities

Solve the system of equations using substitution. - {xy=20x+y=9\left\{ \begin{array} { l } x y = 20 \\x + y = 9\end{array} \right.{xy=20x+y=9​

Solve the system of equations using substitution. - {y=−x2+3x2+y2=5\left\{ \begin{array} { l } y = - x ^ { 2 } + 3 \\x ^ { 2 } + y ^ { 2 } = 5\end{array} \right.{y=−x2+3x2+y2=5​

2x + 3y ≥6 - +y\leq1 -y\leq3

Solve the system of equations using substitution. - {xy−x2=−20x−2y=3\left\{ \begin{array} { l } x y - x ^ { 2 } = - 20 \\x - 2 y = 3\end{array} \right.{xy−x2=−20x−2y=3​

Write the augmented matrix for the system. - {4x+9y+2z=30−2x+6y+2z=09x+6y+5z=38\left\{ \begin{aligned}4 x + 9 y + 2 z & = 30 \\- 2 x + 6 y + 2 z & = 0 \\9 x + 6 y + 5 z & = 38\end{aligned} \right.⎩⎨⎧​4x+9y+2z−2x+6y+2z9x+6y+5z​=30=0=38​

Solve the system of equations. - {x−y+3z=−43x+z=0−x+y−3z=16\left\{ \begin{array} { l } x - y + 3 z = - 4 \\3 x + z = 0 \\- x + y - 3 z = 16\end{array} \right.⎩⎨⎧​x−y+3z=−43x+z=0−x+y−3z=16​

Choose the one alternative that best completes the statement or answers the question. Find the value of the determinant. - ∣12−7−43∣\left| \begin{array} { r r } 12 & - 7 \\- 4 & 3\end{array} \right|​12−4​−73​​

Write the word or phrase that best completes each statement or answers the question. - 7x3−2x2(x+1)3\frac { 7 x ^ { 3 } - 2 } { x ^ { 2 } ( x + 1 ) ^ { 3 } }x2(x+1)37x3−2​

Write the word or phrase that best completes each statement or answers the question. Solve for x. - ∣8x25∣=32\left| \begin{array} { l l } 8 & x \\2 & 5\end{array} \right| = 32​82​x5​​=32