Question 1

$\left\{ \begin{array} { l } 
x y = 30 \
x + y = 11
\end{array} \right.$

Accepted Answer

A)   (6,-5),(5,-6) 
B)   (-6,-5),(-5,-6) 
C)   (6,5),(5,6) 
D)   (-6,5),(-5,6) 
A)   (6,-5),(5,-6) 
B)   (-6,-5),(-5,-6) 
C)   (6,5),(5,6) 
D)   (-6,5),(-5,6)

Question 2

We have encoded a message by assigning the numbers 1 - 26 to the letters a - z of the alphabet, respectively, and
assigning 27 to a blank space. We have further encoded it by using an encoding matrix. Decode this message by finding
the inverse of the encoding matrix and multiplying it times the coded message.
-The encoding matrix i $$A = \left[ \begin{array} { l l l } 
1 & 2 & 2 \
1 & 3 & 2 \
1 & 2 & 3
\end{array} \right] \text { and the encoded message is } 88,103,115,84,99,104,41,43,46,40,49,45$$ 86, 91, 113, 52, 61, 65.

Accepted Answer

The answer of We have encoded a message by assigning...

Question 3

We can encode a message by assigning the numbers 1 - 26 to the letters a - z of the alphabet, respectively, and assigning
27 to a blank space. To further encode a message, we can use an encoding matrix A to convert these numbers into new
pairs or triples of numbers. Use matrix A to encode the given message.
-Use the matrix A $$A = \left[ \begin{array} { r c c } 
4 & 2 & - 2 \
- 3 & 1 & 2 \
3 & - 2 & 1
\end{array} \right]$$ to encode the message "Thank you" into triples of numbers. Combine the triples
of numbers to give the encoded numerical message.

Accepted Answer

94, -50, 4

Question 4

Find the indicated sum or difference, if it is defined.
-$\left[ \begin{array} { l l l } - 2 & 9 & 1 \end{array} \right] - \left[ \begin{array} { l l } 4 & 3 \end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { l l l } - 6 & 9 & - 2 \end{array} \right]$ 
B)  not defined 
C)  $\left[ \begin{array} { l l l } - 6 & 6 & - 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } - 6 & 6 & 1 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l l } - 6 & 9 & - 2 \end{array} \right]$ 
B)  not defined 
C)  $\left[ \begin{array} { l l l } - 6 & 6 & - 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } - 6 & 6 & 1 \end{array} \right]$

Question 5

Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The total income from the 5% and 6% investments is equal to the income
From the 8% investment. Find the amount invested at each rate.

Accepted Answer

A)  $10,000 at 5%, $10,000 at 6%, $5000 at 8% 
B)  $5000 at 5%, $10,000 at 6%, $10,000 at 8% 
C)  $10,000 at 5%, $5000 at 6%, $10,000 at 8% 
D)  $8000 at 5%, $10,000 at 6%, $7000 at 8% 
A)  $10,000 at 5%, $10,000 at 6%, $5000 at 8% 
B)  $5000 at 5%, $10,000 at 6%, $10,000 at 8% 
C)  $10,000 at 5%, $5000 at 6%, $10,000 at 8% 
D)  $8000 at 5%, $10,000 at 6%, $7000 at 8%

Question 6

$A = \left[ \begin{array} { l l l } 
- 7 & - 2 & 5
\end{array} \right] \text { and } B = \left[ \begin{array} { r r r } 
- 1 & - 3 & - 9 \
1 & 2 & - 4 \
1 & - 2 & - 2
\end{array} \right]$

Accepted Answer

A) $\text { [10 } 7 \text { 61] }$ 
B) $\left[ \begin{array} { r r r } 
7 & 6 & - 45 \
- 7 & - 4 & - 20 \
- 7 & 4 & - 10
\end{array} \right]$ 
C)  not possible 
D)  $\left[ \begin{array} { r } 
10 \
7 \
61
\end{array} \right]$ 
A) $\text { [10 } 7 \text { 61] }$ 
B) $\left[ \begin{array} { r r r } 
7 & 6 & - 45 \
- 7 & - 4 & - 20 \
- 7 & 4 & - 10
\end{array} \right]$ 
C)  not possible 
D)  $\left[ \begin{array} { r } 
10 \
7 \
61
\end{array} \right]$

Question 7

Find the inverse matrix of A.
-$$A = \left[ \begin{array} { r r } 
- 2 & 3 \
- 6 & - 6
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } - \frac { 1 } { 5 } & \frac { 1 } { 10 } \ - \frac { 1 } { 5 } & - \frac { 1 } { 15 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c } \frac { 1 } { 5 } - \frac { 1 } { 15 } \ - \frac { 1 } { 5 } - \frac { 1 } { 10 } \end{array} \right]$ 
C) 
$\left[\begin{array}{r}
-\frac{1}{15}-\frac{1}{10} \
\frac{1}{5}-\frac{1}{5}
\end{array}\right]$ 
D)  $\left[ \begin{array} { c } - \frac { 1 } { 5 } - \frac { 1 } { 10 } \ \frac { 1 } { 5 } - \frac { 1 } { 15 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } - \frac { 1 } { 5 } & \frac { 1 } { 10 } \ - \frac { 1 } { 5 } & - \frac { 1 } { 15 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c } \frac { 1 } { 5 } - \frac { 1 } { 15 } \ - \frac { 1 } { 5 } - \frac { 1 } { 10 } \end{array} \right]$ 
C) 
$\left[\begin{array}{r}
-\frac{1}{15}-\frac{1}{10} \
\frac{1}{5}-\frac{1}{5}
\end{array}\right]$ 
D)  $\left[ \begin{array} { c } - \frac { 1 } { 5 } - \frac { 1 } { 10 } \ \frac { 1 } { 5 } - \frac { 1 } { 15 } \end{array} \right]$

Question 8

A company offers three mutual fund plans for its employees. Plan I consists of 2 blocks of common stocks, 3 municipal bonds, and 4 blocks of preferred stock. Plan II consists of 2 blocks of common stocks, 2 municipal
Bonds, and 1 block of preferred stock. Plan III consists of 4 blocks of common stocks, 5 municipal bonds, and 5
Blocks of preferred stock. An employee combined these plans so that he has 22 blocks of common stock, 27
Municipal bonds, and 26 blocks of preferred stock. How many units of plan III might he have?

Accepted Answer

A)  0, 1, 2, 3, 4, or 5 
B)  3, 4, 5, or 6 
C)  0, 1, 2, 3, 4, 5, or 6 
D)  3, 4, or 5 
A)  0, 1, 2, 3, 4, or 5 
B)  3, 4, 5, or 6 
C)  0, 1, 2, 3, 4, 5, or 6 
D)  3, 4, or 5

Question 9

Decide whether or not matrix A and matrix B are inverses.
-$$\mathrm { A } = \left[ \begin{array} { r r } 
- 2 & 4 \
4 & - 4
\end{array} \right] \text { and } \mathrm { B } = \left[ \begin{array} { l l } 
1 / 2 & 1 / 4 \
1 / 2 & 1 / 4
\end{array} \right]$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 10

Use an inverse matrix to find the solution to the system.
-$$\left\{ \begin{array} { c } 
- 5 x - y - 7 z = - 35 \
- 6 x + 6 z = - 12 \
5 y + z = 7
\end{array} \right.$$

Accepted Answer

A)  $x = - 4 , y = 8 , z = 1$ 
B)  $x = 4 , y = 1 , z = 2$ 
C)  $x = 4 , y = 2 , z = 1$ 
D)  $x = - 4 , y = 1 , z = 8$ 
A)  $x = - 4 , y = 8 , z = 1$ 
B)  $x = 4 , y = 1 , z = 2$ 
C)  $x = 4 , y = 2 , z = 1$ 
D)  $x = - 4 , y = 1 , z = 8$

Question 11

$\left\{ \begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 39 \
x - y = 3
\end{array} \right.$

Accepted Answer

A)   (8,-5) 
B)   (-8,5) 
C)   (8,5) 
D)   (-8,-5) 
A)   (8,-5) 
B)   (-8,5) 
C)   (8,5) 
D)   (-8,-5)

Question 12

Solve for x.
-$$\left| \begin{array} { l l } 
2 & 4 \
x & 3
\end{array} \right| = - 2$$

Accepted Answer

A)  2 
B)  $- 1$ 
C)  $- 2$ 
D)  No solution 
A)  2 
B)  $- 1$ 
C)  $- 2$ 
D)  No solution

Question 13

Find the solution or solutions, if any exist, to the system.
-$$\left\{ \begin{array} { l } 
7 x + 7 y + z = 1 \
x + 8 y + 8 z = 8 \
9 x + y + 9 z = 9
\end{array} \right.$$

Accepted Answer

A)  $x = 0 , y = 1 , z = 0$ 
B)  $x = - 1 , y = 1 , z = 1$ 
C)  $x = 1 , y = - 1 , z = 1$ 
D)  $x = 0 , y = 0 , z = 1$ 
A)  $x = 0 , y = 1 , z = 0$ 
B)  $x = - 1 , y = 1 , z = 1$ 
C)  $x = 1 , y = - 1 , z = 1$ 
D)  $x = 0 , y = 0 , z = 1$

Question 14

Solve the system graphically.
-A rectangular metal sheet has an area of 150 square centimeters. Four squares with sides $2 \mathrm {~cm}$ are cut from the corners of the sheet, and the edges are bent upward to form an open box with a volume of 132 cubic centimeters. Find the dimensions of the box.

Accepted Answer

A)  Length $= 15 \mathrm {~cm}$; width $= 10 \mathrm {~cm}$; height $= 2 \mathrm {~cm}$ 
B)  Length $= 13 \mathrm {~cm}$; width $= 8 \mathrm {~cm}$; height $= 2 \mathrm {~cm}$ 
C)  Length $= 11 \mathrm {~cm}$; width $= 2 \mathrm {~cm}$; height $= 6 \mathrm {~cm}$ 
D)  Length $= 11 \mathrm {~cm}$; width $= 6 \mathrm {~cm}$; height $= 2 \mathrm {~cm}$ 
A)  Length $= 15 \mathrm {~cm}$; width $= 10 \mathrm {~cm}$; height $= 2 \mathrm {~cm}$ 
B)  Length $= 13 \mathrm {~cm}$; width $= 8 \mathrm {~cm}$; height $= 2 \mathrm {~cm}$ 
C)  Length $= 11 \mathrm {~cm}$; width $= 2 \mathrm {~cm}$; height $= 6 \mathrm {~cm}$ 
D)  Length $= 11 \mathrm {~cm}$; width $= 6 \mathrm {~cm}$; height $= 2 \mathrm {~cm}$

Question 15

first two games of the season. Write a matrix containing the total number of points and rebounds for each of the starting
five. 
$$\begin{array}{l}
\begin{array} { l | c | c } 
\text { Game } 1 & \text { Points } & \text { Rebounds } \
\hline \text { Levy } & 20 & 3 \
\text { Cowens } & 16 & 5 \
\text { Williams } & 8 & 12 \
\text { Miller } & 6 & 11 \
\text { Jenkins } & 10 & 2
\end{array}\\
\begin{array} { l | c | c } 
\text { Game } 2 & \text { Points } & \text { Rebounds } \
\hline \text { Levy } & 18 & 4 \
\text { Cowens } & 14 & 3 \
\text { Williams } & 12 & 9 \
\text { Miller } & 4 & 10 \
\text { Jenkins } & 10 & 3
\end{array}
\end{array}$$

Accepted Answer

A)  $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$
В) $\left[ \begin{array} { r r } 7 & 38 \ 30 & 8 \ 21 & 20 \ 21 & 10 \ 5 & 20 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 38 & 7 \ 30 & 8 \ 20 & 21 \ 10 & 21 \ 20 & 5 \end{array} \right]$ 
D)  $[ 625 ]$ Answer: C
-The table below gives the median annual incomes for men and women in three cities in 2001. Assume that in 2002, the median annual incomes increased by 7% in all categories. Create a matrix that represents the median
Annual incomes for 2002. Round numbers to the nearest dollar. $$\begin{array} { l | l | l } 
& \text { Men } & \text { Women } \
\hline \text { City 1 } & \$ 35,562 & \$ 31,652 \
\text { City 2 } & 31,277 & 26,433 \
\text { City 3 } & 26,571 & 24,140
\end{array}$$ 
A)  $\left[ \begin{array} { l l } 33,073 & 29,436 \ 29,088 & 24,583 \ 24,711 & 22,450 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 2489 & 2216 \ 2189 & 1850 \ 1860 & 1690 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } 38,051 & 29,436 \ 33,466 & 24,583 \ 28,431 & 22,450 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 38,051 & 33,868 \ 33,466 & 28,283 \ 28,431 & 25,830 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$
В) $\left[ \begin{array} { r r } 7 & 38 \ 30 & 8 \ 21 & 20 \ 21 & 10 \ 5 & 20 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 38 & 7 \ 30 & 8 \ 20 & 21 \ 10 & 21 \ 20 & 5 \end{array} \right]$ 
D)  $[ 625 ]$ Answer: C
-The table below gives the median annual incomes for men and women in three cities in 2001. Assume that in 2002, the median annual incomes increased by 7% in all categories. Create a matrix that represents the median
Annual incomes for 2002. Round numbers to the nearest dollar. $$\begin{array} { l | l | l } 
& \text { Men } & \text { Women } \
\hline \text { City 1 } & \$ 35,562 & \$ 31,652 \
\text { City 2 } & 31,277 & 26,433 \
\text { City 3 } & 26,571 & 24,140
\end{array}$$ 
A)  $\left[ \begin{array} { l l } 33,073 & 29,436 \ 29,088 & 24,583 \ 24,711 & 22,450 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 2489 & 2216 \ 2189 & 1850 \ 1860 & 1690 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } 38,051 & 29,436 \ 33,466 & 24,583 \ 28,431 & 22,450 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 38,051 & 33,868 \ 33,466 & 28,283 \ 28,431 & 25,830 \end{array} \right]$

Question 16

A basketball fieldhouse seats 15,000. Courtside seats sell for $8, endzone for $7, and balcony for $5. A full house earns $88,000 in ticket revenue. If half the courtside and balcony seats and all the endzone seats are sold, the
Total ticket revenue is $51,000. How many of each type of seat are there?

Accepted Answer

A)  4000 courtside, 3000 endzone, 8000 balcony 
B)  4000 courtside, 1500 endzone, 9500 balcony 
C)  3200 courtside, 1800 endzone, 10,000 balcony 
D)  3000 courtside, 2000 endzone, 10,000 balcony 
A)  4000 courtside, 3000 endzone, 8000 balcony 
B)  4000 courtside, 1500 endzone, 9500 balcony 
C)  3200 courtside, 1800 endzone, 10,000 balcony 
D)  3000 courtside, 2000 endzone, 10,000 balcony

Question 17

A psychologist studying the effects of good nutrition on the behavior of rabbits feeds one group a combination of three foods, I, II, and III. Each of these foods contains three additives, A, B, and C, that are used in the study.
The table below gives the percent of each additive that is present in each food. If the diet being used requires
19)1 g per day of A, 8.94 g of B, and 14.02 g of C, find the number of grams of food II that should be used each
Day) Let z represent the number of grams of food III. $\begin{array}{l|l|l|l} 
& \text { Food I| Food II } & \text { Food III } \
\hline \text { Additive A } & 10 \% & 10 \% & 11 \% \
\text { Additive B } & 6 \% & 2 \% & 15 \% \
\text { Additive C } & 8 \% & 6 \% & 13 \%
\end{array}$

Accepted Answer

A)  $2.7 \mathrm { z } - 60$ 
B)  $1.8 z + 54$ 
C)  $128 - 3.2 \mathrm { z }$ 
D)  $2.1 z + 63$ 
A)  $2.7 \mathrm { z } - 60$ 
B)  $1.8 z + 54$ 
C)  $128 - 3.2 \mathrm { z }$ 
D)  $2.1 z + 63$

Question 18

Find the value of the determinant.
-$\left| \begin{array} { l l } 4 & - 3 \ 0 & 1 \end{array} \right|$

Accepted Answer

A)  $- 12$ 
B)  7 
C)  4 
D)  $- 4$ 
A)  $- 12$ 
B)  7 
C)  4 
D)  $- 4$

Question 19

first two games of the season. Write a matrix containing the total number of points and rebounds for each of the starting
five. 
$$\begin{array}{l}
\begin{array} { l | c | c } 
\text { Game } 1 & \text { Points } & \text { Rebounds } \
\hline \text { Levy } & 20 & 3 \
\text { Cowens } & 16 & 5 \
\text { Williams } & 8 & 12 \
\text { Miller } & 6 & 11 \
\text { Jenkins } & 10 & 2
\end{array}\\
\begin{array} { l | c | c } 
\text { Game } 2 & \text { Points } & \text { Rebounds } \
\hline \text { Levy } & 18 & 4 \
\text { Cowens } & 14 & 3 \
\text { Williams } & 12 & 9 \
\text { Miller } & 4 & 10 \
\text { Jenkins } & 10 & 3
\end{array}
\end{array}$$

Accepted Answer

A)  $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$
В) $\left[ \begin{array} { r r } 7 & 38 \ 30 & 8 \ 21 & 20 \ 21 & 10 \ 5 & 20 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 38 & 7 \ 30 & 8 \ 20 & 21 \ 10 & 21 \ 20 & 5 \end{array} \right]$ 
D)  $[ 625 ]$ Answer: C
-Barnes and Able are partners that sell life, health, and auto insurance. The tables below show their sales figures for May and June. Find the matrix that gives total sales for the two months.
 $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { May Sales (\$) }$
$\begin{array}{l|l|r|l} 
& \text { Life } & \text { Health } & \text { Auto } \
\hline \text { Able } & 20,000 & 15,000 & 7000 \
\text { Barnes } & 30,000 & 0 & 17,000
\end{array}$

$\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\text { June Sales (\$) }$
$\begin{array}{l|l|r|l} 
& \text { Life } & \text { Health } & \text { Auto } \
\hline \text { Able } & 70,000 & 0 & 30,000 \
\text { Barnes } & 30,000 & 22,000 & 32,000
\end{array}$ 
A)  $\left[ \begin{array} { l l l } 90,000 & 15,000 & 37,000 \ 60,000 & 22,000 & 49,000 \end{array} \right]$ 
B)  $[ 150,00022,00049,000 ]$ 
C)  $\left[ \begin{array} { l l l } 90,000 & 15,000 & 37,000 \ 60,000 & 22,000 & 32,000 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } 90,000 & 0 & 37,000 \ 60,000 & 0 & 49,000 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$
В) $\left[ \begin{array} { r r } 7 & 38 \ 30 & 8 \ 21 & 20 \ 21 & 10 \ 5 & 20 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 38 & 7 \ 30 & 8 \ 20 & 21 \ 10 & 21 \ 20 & 5 \end{array} \right]$ 
D)  $[ 625 ]$ Answer: C
-Barnes and Able are partners that sell life, health, and auto insurance. The tables below show their sales figures for May and June. Find the matrix that gives total sales for the two months.
 $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { May Sales (\$) }$
$\begin{array}{l|l|r|l} 
& \text { Life } & \text { Health } & \text { Auto } \
\hline \text { Able } & 20,000 & 15,000 & 7000 \
\text { Barnes } & 30,000 & 0 & 17,000
\end{array}$

$\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\text { June Sales (\$) }$
$\begin{array}{l|l|r|l} 
& \text { Life } & \text { Health } & \text { Auto } \
\hline \text { Able } & 70,000 & 0 & 30,000 \
\text { Barnes } & 30,000 & 22,000 & 32,000
\end{array}$ 
A)  $\left[ \begin{array} { l l l } 90,000 & 15,000 & 37,000 \ 60,000 & 22,000 & 49,000 \end{array} \right]$ 
B)  $[ 150,00022,00049,000 ]$ 
C)  $\left[ \begin{array} { l l l } 90,000 & 15,000 & 37,000 \ 60,000 & 22,000 & 32,000 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } 90,000 & 0 & 37,000 \ 60,000 & 0 & 49,000 \end{array} \right]$

Question 20

Solve the system graphically.
-$$\left\{ \begin{array} { l } 
x y + 5 x = 24 \
\frac { y } { x } + y = \frac { 5 } { 4 }
\end{array} \right.$$

Accepted Answer

A)  $\left( - \frac { 3 } { 4 } , - 4 \right)$ 
B)  $\left( \frac { 19 } { 4 } , \frac { 1 } { 25 } \right) , ( - 1 , - 29 )$ 
C)  $( 4,1 ) , \left( - \frac { 24 } { 25 } , - 30 \right)$ 
D)  $( 4,1 )$ 
A)  $\left( - \frac { 3 } { 4 } , - 4 \right)$ 
B)  $\left( \frac { 19 } { 4 } , \frac { 1 } { 25 } \right) , ( - 1 , - 29 )$ 
C)  $( 4,1 ) , \left( - \frac { 24 } { 25 } , - 30 \right)$ 
D)  $( 4,1 )$

$\left\{ \begin{array} { l } x y = 30 \\x + y = 11\end{array} \right.$

Find the indicated sum or difference, if it is defined. - $\left[ \begin{array} { l l l } - 2 & 9 & 1 \end{array} \right] - \left[ \begin{array} { l l } 4 & 3 \end{array} \right]$

Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The total income from the 5% and 6% investments is equal to the income From the 8% investment. Find the amount invested at each rate.

$A = \left[ \begin{array} { l l l } - 7 & - 2 & 5\end{array} \right] \text { and } B = \left[ \begin{array} { r r r } - 1 & - 3 & - 9 \\1 & 2 & - 4 \\1 & - 2 & - 2\end{array} \right]$

Find the inverse matrix of A. - $A = \left[ \begin{array} { r r } - 2 & 3 \\- 6 & - 6\end{array} \right]$

Decide whether or not matrix A and matrix B are inverses. - $\mathrm { A } = \left[ \begin{array} { r r } - 2 & 4 \\4 & - 4\end{array} \right] \text { and } \mathrm { B } = \left[ \begin{array} { l l } 1 / 2 & 1 / 4 \\1 / 2 & 1 / 4\end{array} \right]$

Use an inverse matrix to find the solution to the system. - $\left\{ \begin{array} { c } - 5 x - y - 7 z = - 35 \\- 6 x + 6 z = - 12 \\5 y + z = 7\end{array} \right.$

$\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 39 \\x - y = 3\end{array} \right.$

Solve for x. - $\left| \begin{array} { l l } 2 & 4 \\x & 3\end{array} \right| = - 2$

Find the solution or solutions, if any exist, to the system. - $\left\{ \begin{array} { l } 7 x + 7 y + z = 1 \\x + 8 y + 8 z = 8 \\9 x + y + 9 z = 9\end{array} \right.$

Solve the system graphically. -A rectangular metal sheet has an area of 150 square centimeters. Four squares with sides $2 \mathrm {~cm}$ are cut from the corners of the sheet, and the edges are bent upward to form an open box with a volume of 132 cubic centimeters. Find the dimensions of the box.

Find the value of the determinant. - $\left| \begin{array} { l l } 4 & - 3 \\ 0 & 1 \end{array} \right|$

Solve the system graphically. - $\left\{ \begin{array} { l } x y + 5 x = 24 \\\frac { y } { x } + y = \frac { 5 } { 4 }\end{array} \right.$ $Solve the system graphically. - \left\{ \begin{array} { l } x y + 5 x = 24 \\ \frac { y } { x } + y = \frac { 5 } { 4 } \end{array} \right.$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Special Topics in Algebra

Filters

Exam 7: Systems of Equations and Matrices

{xy=30x+y=11\left\{ \begin{array} { l } x y = 30 \\x + y = 11\end{array} \right.{xy=30x+y=11​

Find the indicated sum or difference, if it is defined. - [−291]−[43]\left[ \begin{array} { l l l } - 2 & 9 & 1 \end{array} \right] - \left[ \begin{array} { l l } 4 & 3 \end{array} \right][−2​9​1​]−[4​3​]