Question 1

Graph the system of inequalities.
-

Accepted Answer

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

Question 2

Graph the system of inequalities.
-$\left\{\begin{array}{l}
x^{2}+y^{2} \leq 81 \
6 x+3 y \leq 18
\end{array}\right.$

Accepted Answer

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

Question 3

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 74 \
x ^ { 2 } - y ^ { 2 } = 24
\end{array} \right.$$

Accepted Answer

A)  $x = 7 , y = 5 ; x = 5 , y = 7 ; x = - 7 , y = - 5 ; x = - 5 , y = - 7$ 
B)  $x = - 7 , y = - 5 ; x = - 5 , y = - 7$ 
C)  $x = 7 , y = 5 ; x = - 7 , y = 5 ; x = 7 , y = - 5 ; x = - 7 , y = - 5$ 
D)  $x = 7 , y = - 5 ; x = 7 , y = 5$ 
A)  $x = 7 , y = 5 ; x = 5 , y = 7 ; x = - 7 , y = - 5 ; x = - 5 , y = - 7$ 
B)  $x = - 7 , y = - 5 ; x = - 5 , y = - 7$ 
C)  $x = 7 , y = 5 ; x = - 7 , y = 5 ; x = 7 , y = - 5 ; x = - 7 , y = - 5$ 
D)  $x = 7 , y = - 5 ; x = 7 , y = 5$

Question 4

Solve the problem.
-Let $\mathrm { A } = \left[ \begin{array} { r r r } 6 & - 1 & - 2 \ - 4 & 7 & - 2 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r r } 7 & 6 & 2 \ - 7 & 7 & - 9 \ - 4 & - 9 & 7 \end{array} \right]$. Find $\mathrm { AB }$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } 6 & - 1 & - 2 \ - 4 & 7 & - 2 \ 7 & 7 & - 2 \ - 7 & 7 & - 9 \ - 4 & - 4 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 57 & 47 & 7 \ - 69 & 43 & - 85 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 42 & - 6 & - 4 \ 28 & 49 & 18 \ 16 & - 63 & - 14 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 57 & - 69 \ 47 & 43 \ 7 & - 85 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 6 & - 1 & - 2 \ - 4 & 7 & - 2 \ 7 & 7 & - 2 \ - 7 & 7 & - 9 \ - 4 & - 4 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 57 & 47 & 7 \ - 69 & 43 & - 85 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 42 & - 6 & - 4 \ 28 & 49 & 18 \ 16 & - 63 & - 14 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 57 & - 69 \ 47 & 43 \ 7 & - 85 \end{array} \right]$

Question 5

Graph the system of inequalities.
-$\left\{\begin{array}{r}
2 x+3 y \geq 6 \
x-y \leq 3 \
y \leq 2
\end{array}\right.$

Accepted Answer

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

Question 6

Solve the system of equations by using substitution.
-$$\left\{ \begin{array} { l } 
3 x + y = 13 \
2 x + 9 y = - 8
\end{array} \right.$$

Accepted Answer

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

Question 7

Find the inverse of the matrix.
-$$\left[ \begin{array} { l l l } 
1 & 1 & 1 \
2 & 1 & 1 \
2 & 2 & 3
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } - 1 & - 1 & - 1 \ - 2 & - 1 & - 1 \ - 2 & - 2 & - 3 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 1 & 1 & 0 \ 4 & - 1 & - 1 \ - 2 & 0 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 1 & 1 & 1 \ \frac { 1 } { 2 } & 1 & 1 \ \frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 } \end{array} \right]$ 
D)  No inverse 
A)  $\left[ \begin{array} { l l l } - 1 & - 1 & - 1 \ - 2 & - 1 & - 1 \ - 2 & - 2 & - 3 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 1 & 1 & 0 \ 4 & - 1 & - 1 \ - 2 & 0 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 1 & 1 & 1 \ \frac { 1 } { 2 } & 1 & 1 \ \frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 } \end{array} \right]$ 
D)  No inverse

Question 8

Write the augmented matrix for the system.
-$$\left\{ \begin{array} { r } 
- 2 x + 8 y = 28 \
5 y = 20
\end{array} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { r | r | r } 5 & 0 & 20 \ - 2 & 8 & 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 28 & 8 & - 2 \ 20 & 0 & 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 2 & 8 & 28 \ 0 & 5 & 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } - 2 & 8 & 28 \ 5 & 20 & 0 \end{array} \right]$ 
A)  $\left[ \begin{array} { r | r | r } 5 & 0 & 20 \ - 2 & 8 & 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 28 & 8 & - 2 \ 20 & 0 & 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 2 & 8 & 28 \ 0 & 5 & 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } - 2 & 8 & 28 \ 5 & 20 & 0 \end{array} \right]$

Question 9

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r } 
6 & 1 \
- 2 & 0
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r } 0 & - \frac { 1 } { 2 } \ 1 & 3 \end{array} \right]$ 
B)  $\left[ \begin{array} { l r } 1 & 3 \ 0 & - \frac { 1 } { 2 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 0 & \frac { 1 } { 2 } \ - 1 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 3 & - \frac { 1 } { 2 } \ 1 & 0 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 0 & - \frac { 1 } { 2 } \ 1 & 3 \end{array} \right]$ 
B)  $\left[ \begin{array} { l r } 1 & 3 \ 0 & - \frac { 1 } { 2 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 0 & \frac { 1 } { 2 } \ - 1 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 3 & - \frac { 1 } { 2 } \ 1 & 0 \end{array} \right]$

Question 10

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r } 
3 & 0 \
1 & - 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } - 1 & 0 \ \frac { 1 } { 3 } & \frac { 1 } { 3 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } \frac { 1 } { 3 } & 0 \ - \frac { 1 } { 3 } & - 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } \frac { 1 } { 3 } & 0 \ \frac { 1 } { 3 } & - 1 \end{array} \right]$ 
D)  No inverse 
A)  $\left[ \begin{array} { c c } - 1 & 0 \ \frac { 1 } { 3 } & \frac { 1 } { 3 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } \frac { 1 } { 3 } & 0 \ - \frac { 1 } { 3 } & - 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } \frac { 1 } { 3 } & 0 \ \frac { 1 } { 3 } & - 1 \end{array} \right]$ 
D)  No inverse

Question 11

Solve the problem.
-A rectangular piece of tin has an area of 592 square inches. A square of 4 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 928 cubic inches, what were the
Original dimensions of the piece of tin?

Accepted Answer

A)  8 in. by 25 in. 
B)  20 in. by 41 in. 
C)  16 in. by 37 in. 
D)  12 in. by 33 in. 
A)  8 in. by 25 in. 
B)  20 in. by 41 in. 
C)  16 in. by 37 in. 
D)  12 in. by 33 in.

Question 12

Solve the system.
-$$\left\{ \begin{array} { l } 
x - 4 y = - 10 \
2 x - 8 y = - 17
\end{array} \right.$$

Accepted Answer

A)  dependent (many solutions) 
B)  (2, 4) 
C)  (2, 3) 
D)  inconsistent (no solution) 
A)  dependent (many solutions) 
B)  (2, 4) 
C)  (2, 3) 
D)  inconsistent (no solution)

Question 13

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 39 \
x - y = 3
\end{array} \right.$$

Accepted Answer

A)  $x = - 8 , y = - 5$ 
B)  $x = - 8 , y = 5$ 
C)  $x = 8 , y = 5$ 
D)  $x = 8 , y = - 5$ 
A)  $x = - 8 , y = - 5$ 
B)  $x = - 8 , y = 5$ 
C)  $x = 8 , y = 5$ 
D)  $x = 8 , y = - 5$

Question 14

Graph the inequality.
-

Accepted Answer

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

Question 15

Find the value of the determinant.
-$$\left| \begin{array} { l l l } 
4 & 4 & 6 \
3 & 4 & 5 \
4 & 4 & 4
\end{array} \right|$$

Accepted Answer

A)  -8 
B)  -168 
C)  8 
D)  440 
A)  -8 
B)  -168 
C)  8 
D)  440

Question 16

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary.
-$$\left[ \begin{array} { r r r } 
- 16 & 3 & 28 \
5 & - 14 & 15 \
34 & 25 & 2
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 0.01 & 0.02 & 0.01 \ 0.02 & - 0.03 & 0.01 \ 0.02 & 0.02 & 0 . \end{array} \right.$ 
B)  $\left[ \begin{array} { r r r } - 0.02 & 0.03 & 0.02 \ 0.02 & - 0.04 & 0.01 \ 0.02 & 0.02 & 0.00 \end{array} \right]$ 
C)  
$ \left[\begin{array}{rrr}-0.01 & 0.03 & 0.02 \ 0.02 & -0.03 & 0.01 \ 0.02 & 0.02 & 0.01\end{array}\right] $ 
D) 
$ \left[\begin{array}{rrr}-0.02 & 0.03 & 0.02 \ 0.02 & -0.04 & 0.02 \ 0.02 & 0.02 & 0.01\end{array}\right] $ 
A)  $\left[ \begin{array} { r r r } - 0.01 & 0.02 & 0.01 \ 0.02 & - 0.03 & 0.01 \ 0.02 & 0.02 & 0 . \end{array} \right.$ 
B)  $\left[ \begin{array} { r r r } - 0.02 & 0.03 & 0.02 \ 0.02 & - 0.04 & 0.01 \ 0.02 & 0.02 & 0.00 \end{array} \right]$ 
C)  
$ \left[\begin{array}{rrr}-0.01 & 0.03 & 0.02 \ 0.02 & -0.03 & 0.01 \ 0.02 & 0.02 & 0.01\end{array}\right] $ 
D) 
$ \left[\begin{array}{rrr}-0.02 & 0.03 & 0.02 \ 0.02 & -0.04 & 0.02 \ 0.02 & 0.02 & 0.01\end{array}\right] $

Question 17

Write the partial fraction decomposition of the rational expression.
-$\frac { 2 x ^ { 3 } + 4 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Accepted Answer

A)  $\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { 10 x - 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
B)  $\frac { 2 x - 4 } { x ^ { 2 } + 5 } + \frac { - 10 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
C)  $\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { - 10 x - 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
D)  $\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { 10 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
A)  $\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { 10 x - 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
B)  $\frac { 2 x - 4 } { x ^ { 2 } + 5 } + \frac { - 10 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
C)  $\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { - 10 x - 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
D)  $\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { 10 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Question 18

Graph the system of inequalities.
-$$\begin{array} { l } 
y \geq x ^ { 2 } \
x + y > 6
\end{array}$$

Accepted Answer

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

Question 19

Verify that the values of the variables listed are solutions of the system of equations.
-$$\begin{array} { l } 
\left\{ \begin{array} { l } 
2 x + y = 6 \
3 x + 2 y = 7
\end{array} \right. \
x = 5 , y = - 4
\end{array}$$

Accepted Answer

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

Question 20

Verify that the values of the variables listed are solutions of the system of equations.
-$$\left\{ \begin{array} { l } 
x + y = - 1 \
x - y = 11 \
\end{array} \right.$$

x = 5 , y = - 6

Accepted Answer

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

Graph the system of inequalities. -

Graph the system of inequalities. - $\left\{\begin{array}{l}x^{2}+y^{2} \leq 81 \\6 x+3 y \leq 18\end{array}\right.$ $Graph the system of inequalities. - \left\{\begin{array}{l} x^{2}+y^{2} \leq 81 \\ 6 x+3 y \leq 18 \end{array}\right.$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 74 \\x ^ { 2 } - y ^ { 2 } = 24\end{array} \right.$

Solve the problem. -Let $\mathrm { A } = \left[ \begin{array} { r r r } 6 & - 1 & - 2 \\ - 4 & 7 & - 2 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r r } 7 & 6 & 2 \\ - 7 & 7 & - 9 \\ - 4 & - 9 & 7 \end{array} \right]$ . Find $\mathrm { AB }$ .

Graph the system of inequalities. - $\left\{\begin{array}{r}2 x+3 y \geq 6 \\x-y \leq 3 \\y \leq 2\end{array}\right.$ $Graph the system of inequalities. - \left\{\begin{array}{r} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ y \leq 2 \end{array}\right.$

Solve the system of equations by using substitution. - $\left\{ \begin{array} { l } 3 x + y = 13 \\2 x + 9 y = - 8\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$

Write the augmented matrix for the system. - $\left\{ \begin{array} { r } - 2 x + 8 y = 28 \\5 y = 20\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 6 & 1 \\- 2 & 0\end{array} \right]$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 3 & 0 \\1 & - 1\end{array} \right]$

Solve the problem. -A rectangular piece of tin has an area of 592 square inches. A square of 4 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 928 cubic inches, what were the Original dimensions of the piece of tin?

$Solve the system. - \left\{ \begin{array} { l } x - 4 y = - 10 \\ 2 x - 8 y = - 17 \end{array} \right.$ Solve the system. - $\left\{ \begin{array} { l } x - 4 y = - 10 \\2 x - 8 y = - 17\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 39 \\x - y = 3\end{array} \right.$

Graph the inequality. -

Find the value of the determinant. - $\left| \begin{array} { l l l } 4 & 4 & 6 \\3 & 4 & 5 \\4 & 4 & 4\end{array} \right|$

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left[ \begin{array} { r r r } - 16 & 3 & 28 \\5 & - 14 & 15 \\34 & 25 & 2\end{array} \right]$

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 3 } + 4 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Graph the system of inequalities. - y\geq x+y>6 $Graph the system of inequalities. - \begin{array} { l } y \geq x ^ { 2 } \\ x + y > 6 \end{array}$

Verify that the values of the variables listed are solutions of the system of equations. - 2x+y=6 3x+2y=7 x=5,y=-4

Verify that the values of the variables listed are solutions of the system of equations. - $\left\{ \begin{array} { l } x + y = - 1 \\x - y = 11 \\\end{array} \right.$ x = 5 , y = - 6

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 6: Systems of Equations and Inequalities

Graph the system of inequalities. -

Graph the system of inequalities. - {x2+y2≤816x+3y≤18\left\{\begin{array}{l}x^{2}+y^{2} \leq 81 \\6 x+3 y \leq 18\end{array}\right.{x2+y2≤816x+3y≤18​

Solve the system of equations using elimination. - {x2+y2=74x2−y2=24\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 74 \\x ^ { 2 } - y ^ { 2 } = 24\end{array} \right.{x2+y2=74x2−y2=24​

Graph the system of inequalities. - {2x+3y≥6x−y≤3y≤2\left\{\begin{array}{r}2 x+3 y \geq 6 \\x-y \leq 3 \\y \leq 2\end{array}\right.⎩⎨⎧​2x+3y≥6x−y≤3y≤2​

Solve the system of equations by using substitution. - {3x+y=132x+9y=−8\left\{ \begin{array} { l } 3 x + y = 13 \\2 x + 9 y = - 8\end{array} \right.{3x+y=132x+9y=−8​

Find the inverse of the matrix. - [111211223]\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]​122​112​113​​

Write the augmented matrix for the system. - {−2x+8y=285y=20\left\{ \begin{array} { r } - 2 x + 8 y = 28 \\5 y = 20\end{array} \right.{−2x+8y=285y=20​

Find the inverse of the matrix. - [61−20]\left[ \begin{array} { r r } 6 & 1 \\- 2 & 0\end{array} \right][6−2​10​]

Find the inverse of the matrix. - [301−1]\left[ \begin{array} { r r } 3 & 0 \\1 & - 1\end{array} \right][31​0−1​]

Solve the problem. -A rectangular piece of tin has an area of 592 square inches. A square of 4 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 928 cubic inches, what were the Original dimensions of the piece of tin?

Solve the system. - {x−4y=−102x−8y=−17\left\{ \begin{array} { l } x - 4 y = - 10 \\2 x - 8 y = - 17\end{array} \right.{x−4y=−102x−8y=−17​

Solve the system of equations using substitution. - {x2−y2=39x−y=3\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 39 \\x - y = 3\end{array} \right.{x2−y2=39x−y=3​

Graph the inequality. -

Find the value of the determinant. - ∣446345444∣\left| \begin{array} { l l l } 4 & 4 & 6 \\3 & 4 & 5 \\4 & 4 & 4\end{array} \right|​434​444​654​​

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - [−163285−141534252]\left[ \begin{array} { r r r } - 16 & 3 & 28 \\5 & - 14 & 15 \\34 & 25 & 2\end{array} \right]​−16534​3−1425​28152​​

Write the partial fraction decomposition of the rational expression. - 2x3+4x2(x2+5)2\frac { 2 x ^ { 3 } + 4 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }(x2+5)22x3+4x2​

Graph the system of inequalities. - y\geq x+y>6

Verify that the values of the variables listed are solutions of the system of equations. - 2x+y=6 3x+2y=7 x=5,y=-4

Verify that the values of the variables listed are solutions of the system of equations. - {x+y=−1x−y=11\left\{ \begin{array} { l } x + y = - 1 \\x - y = 11 \\\end{array} \right.{x+y=−1x−y=11​ x = 5 , y = - 6

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Graph the system of inequalities. - $\left\{\begin{array}{l}x^{2}+y^{2} \leq 81 \\6 x+3 y \leq 18\end{array}\right.$ $Graph the system of inequalities. - \left\{\begin{array}{l} x^{2}+y^{2} \leq 81 \\ 6 x+3 y \leq 18 \end{array}\right.$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 74 \\x ^ { 2 } - y ^ { 2 } = 24\end{array} \right.$

Graph the system of inequalities. - $\left\{\begin{array}{r}2 x+3 y \geq 6 \\x-y \leq 3 \\y \leq 2\end{array}\right.$ $Graph the system of inequalities. - \left\{\begin{array}{r} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ y \leq 2 \end{array}\right.$

Solve the system of equations by using substitution. - $\left\{ \begin{array} { l } 3 x + y = 13 \\2 x + 9 y = - 8\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$

Write the augmented matrix for the system. - $\left\{ \begin{array} { r } - 2 x + 8 y = 28 \\5 y = 20\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 6 & 1 \\- 2 & 0\end{array} \right]$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 3 & 0 \\1 & - 1\end{array} \right]$

$Solve the system. - \left\{ \begin{array} { l } x - 4 y = - 10 \\ 2 x - 8 y = - 17 \end{array} \right.$ Solve the system. - $\left\{ \begin{array} { l } x - 4 y = - 10 \\2 x - 8 y = - 17\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 39 \\x - y = 3\end{array} \right.$

Find the value of the determinant. - $\left| \begin{array} { l l l } 4 & 4 & 6 \\3 & 4 & 5 \\4 & 4 & 4\end{array} \right|$

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left[ \begin{array} { r r r } - 16 & 3 & 28 \\5 & - 14 & 15 \\34 & 25 & 2\end{array} \right]$

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 3 } + 4 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Graph the system of inequalities. - y\geq x+y>6 $Graph the system of inequalities. - \begin{array} { l } y \geq x ^ { 2 } \\ x + y > 6 \end{array}$

Verify that the values of the variables listed are solutions of the system of equations. - $\left\{ \begin{array} { l } x + y = - 1 \\x - y = 11 \\\end{array} \right.$ x = 5 , y = - 6