Deck 7: Systems of Equations and Inequalities

Question 1

Solve the system of equations by substitution.
$$\begin{array} { r } 2 x + 9 y = - 8 \\x + \frac { 1 } { 3 } y = \frac { 13 } { 3 }\end{array}$$

A)(-5, 2)
B)( -5, -2)
C)(5, 2)
D)(5, -2)

Answer 1

D

Question 2

Use Cramer's rule to solve the linear system.
x + y = -7 x - y = 16

A)(4.5, 11.5)
B)(4.5, -11.5)
C)(7, -11.5)
D)(7, 4.5)

Answer 2

B

Question 3

Determine whether the given ordered pair is a solution of the system.
(-6, -4) 4x + y = -28 2x + 4y = -28

A)not a solution
B)solution

Answer 3

B

Question 4

Determine whether the given ordered pair is a solution of the system.
(2, -5) 4x - y = 3 3x - 4y = -14

A)not a solution
B)solution

Question 5

Use Cramer's rule to solve the linear system.
$$\begin{array} { c } \frac { 1 } { 5 } x - y = - \frac { 4 } { 5 } \\x + 8 y = - 4\end{array}$$

A)(0, -4)
B)(0, 4)
C)(-4, 0)
D)(4, 0)

Question 6

Use Cramer's rule to solve the linear system.
$$\begin{array} { l } \frac { 1 } { 2 } x + \frac { 2 } { 3 } y = 32 \\\frac { 1 } { 4 } x - \frac { 5 } { 9 } y = 40\end{array}$$

A)(100, 27)
B)(-100, -27)
C)(100, -27)
D)(-100, 27)

Question 7

Use Cramer's rule to solve the linear system.
x + 7y = -2 3x + y = 34

A)(7, 12)
B)(3, 7)
C)(-2, 3)
D)(12, -2)

Question 8

Use Cramer's rule to solve the linear system.
3x + y = 13 2x - 7y = 24

A)(5, 2)
B)(-5, -2)
C)(-5, 2)
D)(5, -2)

Question 9

Use Cramer's rule to solve the linear system.
9x + y = 0 -9x + y = -18

A)(-1, 9)
B)(1, -9)
C)(-1, -9)
D)(1, 18)

Question 10

Solve the system of equations by substitution.
7x + 64y = 64 4x - 8y = -8

A)(1, 1)
B)(1, 0)
C)(0, 0)
D)(0, 1)

Question 11

Use Cramer's rule to solve the linear system.
(4, 2) 2x + y = 6 3x + 2y = 8

A)not a solution
B)solution

Question 12

Use Cramer's rule to solve the linear system.
x + 3y = 3 2x - 5y = -5

A)(0, 0)
B)(0, 1)
C)(1, 1)
D)(1, 0)

Question 13

Solve the system of equations by substitution.
x + y = -6 x - y = 16

A)(5, 11)
B)(6, 5)
C)(6, -11)
D)(5, -11)

Question 14

Use Cramer's rule to solve the linear system.
x + y = 0 2x + 3y = -7

A)(6, -6)
B)(-7, 7)
C)(-6, 6)
D)(7, -7)

Question 15

Solve the system of equations by substitution.
3x + 6y = 39 3x + 2y = 47

A)(-17, 6)
B)(-2, 17)
C)( -17, 3)
D)(17, -2)

Question 16

Solve the system of equations by substitution.
6x + 3y = 51 2x - 6y = 38

A)(10, -3)
B)(-3, 10)
C)(3, -10)
D)(-10, 3)

Question 17

Use Cramer's rule to solve the linear system.
3x + 2y = -4 5x = -20

A)(4, -4)
B)(-4, -4)
C)(-4, 4)
D)(-4, 0)

Question 18

Use Cramer's rule to solve the linear system.
5x - 2y = -1 x + 4y = 35

A)(3, 9)
B)(2, 8)
C)(2, 9)
D)(3, 8)

Question 19

Determine whether the given ordered pair is a solution of the system.
(6, -3) 2x - y = 9 4x + 2y = 18

A)not a solution
B)solution

Question 20

Use Cramer's rule to solve the linear system.
5x + 3y = 80 2x + y = 30

A)(0, 10)
B)(-10, 10)
C)(10, 0)
D)(10, 10)

Question 21

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
$$\begin{array} { l } ( - 3,1,3 ) \\x + y + z = 1 \\x - y + 2 z = - 4 \\4 x + y + z = 10\end{array}$$

A)solution
B)not a solution

Question 22

Determine if the given ordered triple is a solution of the system.
$$\begin{aligned}7 x - 5 y - z & = 27 \\x - 8 y + 9 z & = 4 \\3 x + y + z & = 33\end{aligned}$$

A)(8, 4, 5)
B)(-8, 5, 16)
C)(16, 5, -8)
D)(8, 5, 4)

Question 23

Solve the system of equations by elimination.
$$\begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 3 } y = 4 \\\frac { 1 } { 4 } x + \frac { 1 } { 6 } y = 2\end{array}$$

A) $( 0,12 )$
B) $\left( - 1 , \frac { 15 } { 2 } \right)$
C) $\left( x , - \frac { 3 } { 2 } x + 12 \right)$ or $\left( - \frac { 2 } { 3 } y + 8 , y \right)$
D) no solution

Question 24

Solve the problem.
The Family Fine Arts Center charges $20 per adult and $11 per senior citizen for its performances. On a recent weekend evening when 514 people paid admission, the total receipts were $7175. How many who paid were senior citizens?

A)259 senior citizens
B)255 senior citizens
C)169 senior citizens
D)345 senior citizens

Question 25

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
$$\begin{array} { l } ( 1,2,3 ) \\5 x + 5 y + z = 18 \\4 x - 2 y - z = - 3 \\4 x + y + 3 z = 15\end{array}$$

A)not a solution
B)solution

Question 26

Solve the system of equations by substitution.
3x - 5y = -12 6x + 8y = -24

A)(0, -4)
B)(0, 4)
C)(-4, 0)
D)(4, 0)

Question 27

Solve the system of equations by substitution.
$$\begin{array} { l } \frac { 7 } { 12 } x - y = 10 \\\frac { 5 } { 9 } x + 2 y = 11\end{array}$$

A) $\left( 16 , \frac { 1 } { 2 } \right)$
B) $\left( - 16 , - \frac { 1 } { 2 } \right)$
C) $\left( - 18 , - \frac { 1 } { 2 } \right)$
D) $\left( 18 , \frac { 1 } { 2 } \right)$

Question 28

Solve the system of equations by elimination.
x + 9y = 9 5x - 6y = -6

A)(1, 1)
B)(0, 0)
C)(1, 0)
D)(0, 1)

Question 29

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
The Paperback Trader is a book store that takes in used paperbacks for 20% of their cover price and sells them for 50% of their cover price. Pat brings in a stack of 17 paperback books to trade and gets $17.17 credit. Some of the books had a cover price of $6.99, the rest $3.99. She wants to get some Tom Clancy books having a cover price of $6.99. How many $6.99 books did she bring in and how many Clancy books can she get without paying any additional cash?

A)6 $6.99 books, 5 Clancy books
B)6 $6.99 books, 2 Clancy books
C)11 $6.99 books, 2 Clancy books
D)6 $6.99 books, 4 Clancy books

Question 30

Solve the system of equations by elimination.
5x + 7y = 22 5x + 2y = 42

A)(-4, 10)
B)(-10, 7)
C)( -10, 5)
D)(10, -4)

Question 31

Determine if the given ordered triple is a solution of the system.
$$\begin{array} { l } ( - 5 , - 1,5 ) \\3 x + 2 y + z = 8 \\2 x - 3 y - z = 18 \\4 x + y + 5 z = - 6\end{array}$$

A)not a solution
B)solution

Question 32

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
$$\begin{array} { c } ( - 5 , - 1,4 ) \\x + y + z = - 2 \\x - y + 3 z = 8 \\5 x + y + z = - 22\end{array}$$

A)solution
B)not a solution

Question 33

Solve the problem.
A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 6 soft drinks for $31.68. The second group bought 5 slices of pizza and 4 soft drinks for $ 20.22. How much does one slice of pizza cost?

A)$2.18 per slice of pizza
B)$1.68 per slice of pizza
C)$2.20 per slice of pizza
D)$2.70 per slice of pizza

Question 34

Solve the system of equations by elimination.
x + 6y = -3 2x + 12y = -6

A)no solution B)
$\left( x , - \frac { 1 } { 6 } x - \frac { 1 } { 2 } \right)$ or $( - 6 y - 3 , y )$
C)(0, 0)
D)(-3, 0)

Question 35

Solve the system of equations by elimination.
3x + y = 6 -6x - 2y = -12 A) $( x , - 3 x + 6 )$ or $\left( - \frac { 1 } { 3 } y + 2 , y \right)$
B) $( x , 3 x + 6 )$ or $\left( \frac { 1 } { 3 } y - 2 , y \right)$
C) no solution
D) $\left( - \frac { 1 } { 3 } x + 2 , x \right)$ or $( y , - 3 y + 6 )$

Question 36

Solve the system of equations by elimination.
6x - 5y = 1 30x - 25y = 4

A)(1, 4)
B)(5, 4) C)
$\left( \frac { 5 } { 36 } , \frac { 1 } { 6 } \right)$
D)no solution

Question 37

Solve the system of equations by elimination.
$$\frac { 3 } { 5 } x + \frac { 2 } { 5 } y = \frac { 38 } { 5 }$$

A)(-16, 6)
B)(16, -5)
C)(-16, 4)
D)(-5, 16)

Question 38

Solve the system of equations by substitution.
2x + 36y = -272 9x + 6y = 24

A)(9, -9)
B)(8, -8)
C)(-8, 8)
D)(-6, 8)

Question 39

Solve the system of equations by elimination.
8x - 5y = 3 -24x + 15y = -12

A)(3, 4)
B)no solution
C)(8, 3) $$\text { D) } \left( \frac { 16 } { 9 } , - \frac { 10 } { 9 } \right)$$

Question 40

Solve the problem.
A flat rectangular piece of aluminum has a perimeter of 62 inches. The length is 9 inches longer than the width. Find the width.

A)29 in.
B)31 in.
C)11 in.
D)20 in.

Question 41

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
$$\begin{array} { r } x - y + 5 z = - 21 \\5 x + z = - 4 \\x + 2 y + z = - 2\end{array}$$

A) $( - 4,0,1 )$
B) no solution
C) $( - 4,1,0 )$
D) $( 0,1 , - 4 )$

Question 42

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
$$\begin{array} { l } 2 x + 5 y + z = - 26 \\3 x - 3 y - z = 21 \\3 x + y + 3 z = - 11\end{array}$$

A)(1, -3, -5)
B)no solution
C)(1, -5, -3)
D)(-3, -5, 1)

Question 43

Solve the system of linear equations using the elimination method.
x + 8y + 8z = 8 7x + 7y + z = 1 8x + 15y + 9z = -9

A)(0, 0, 1)
B)(1, -1, 1)
C)no solution
D)(-1, 0, 1)

Question 44

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
$$\begin{array} { l } x + y + z = 0 \\x - y + 4 z = 0 \\2 x + y + z = 5\end{array}$$

A)(-2, -3, 5)
B)(-2, 5, -3)
C)(5, -3, -2)
D)no solution

Question 45

Determine if the given ordered triple is a solution of the system.
$$\begin{aligned}- 3 x - y - 6 z = & - 75 \\5 x + 5 y - 5 z = & 35 \\- 9 x - 7 y + z = & - 109\end{aligned}$$

A)(-6, 9, 12)
B)(6, 9, 8)
C)(12, 9, -6)
D)(6, 8, 9)

Question 46

Solve the problem.
A basketball player scored 24 points in a game. The number of three-point field goals the player made was 14 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals the player made was 15 more than the number of three-point field goals made. Find the number of free-throws, two-point field goals, and three-point field goals that the player made in the game.

A)5 free throws; 8 two-point field goals; 1 three-point field goals
B)5 free throws; 9 two-point field goals; 3 three-point field goals
C)6 free throws; 8 two-point field goals; 4 three-point field goals
D)5 free throws; 1 two-point field goals; 8 three-point field goals

Question 47

Solve the problem.
The Little Town Arts Center charges $25 for adults, $14 for senior citizens, and $10 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,800 for 792 tickets sold. There were 41 more children than adults. How many children attended?

A)215 children
B)299 children
C)268 children
D)309 children

Question 48

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
$$\begin{aligned}x - y + 5 z & = - 5 \\3 x + z & = 0 \\x + 3 y + z & = 15\end{aligned}$$

A)(0, 5, -5)
B)(0, 0, 5)
C)no solution
D)(0, 5, 0)

Question 49

Solve the system of linear equations using the elimination method.
$$\begin{array} { r r } x + y + z & = 7 \\x - y + 2 z & = 7 \\2 x + 3 z & = 14\end{array}$$

A) $\left( - \frac { 3 z } { 2 } - 7,2 z , z \right)$
B) $\left( - \frac { 3 z } { 2 } + 7 , \frac { z } { 2 } , z \right)$
$C ) \left( - \frac { 3 z } { 2 } - 7 , \frac { z } { 2 } , z \right)$
D) $\left( - \frac { 3 z } { 2 } + 7,2 z , z \right)$

Question 50

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form.
$$\begin{aligned}x + y + z & = 3 \\x - y + 2 z & = 5 \\4 x + y + z & = - 3\end{aligned}$$

A)(-2, 1, 4)
B)(-2, 4, 1)
C)(4, -2, 1)
D)(4, 1, -2)

Question 51

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form.
$$\begin{array} { l } 5 x + 4 y + z = - 16 \\5 x - 2 y - z = - 2 \\4 x + y + 3 z = 7\end{array}$$

A)(-1, 5, -4)
B)no solution
C)(-1, -4, 5)
D)(5, -4, -1)

Question 52

Solve the system of linear equations using the elimination method.
$$\begin{aligned}5 x + 2 y + z & = - 11 \\2 x - 3 y - z & = 17 \\7 x - y & = 12\end{aligned}$$

A)no solution
B)(-2, 0, -1)
C)(0, -6, 1)
D)(1, -5, 0)

Question 53

Solve the problem.
A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A platter takes 16 hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. If the workshop has 119 hours for prep time, 84 hours for painting, and 122 hours for firing, how many of each can be made?

A)9 serving bowls, 5 platters, 3 bread baskets
B)3 serving bowls, 9 platters, 5 bread baskets
C)10 serving bowls, 6 platters, 4 bread baskets
D)5 serving bowls, 3 platters, 9 bread baskets

Question 54

Solve the system of linear equations using the elimination method.
$$\begin{aligned}x + 3 y + 2 z & = 11 \\4 y + 9 z & = - 12 \\x + 7 y + 11 z & = - 1\end{aligned}$$

A) $\left( \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$
B) $\left( - \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$
C) $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } - 3 , \mathrm { z } \right\}$
D) $\left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right)$

Question 55

Solve the problem.
Find the values of $a$ , $b$ , and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 3,5 ) , ( 1,1 )$ , and $( 2 , - 5 )$ .

A) $a = 1 ; b = - 3 ; c = 5$
B) $a = 1 ; b = 5 ; c = - 3$
C) $a = - 1 ; b = 5 ; c = - 3$
D) $a = - 1 ; b = - 3 ; c = 5$

Question 56

Solve the system of linear equations using the elimination method.
x = -5 - y - z x - y + 4z = 2 2x + y =-4 - z

A)(1, -5, -1)
B)(-1, 1, -5)
C)(-1, -5, 1)
D)(-5, -1, 1)

Question 57

Solve the system of linear equations using the elimination method.
$$\begin{aligned}4 x - y + 3 z & = 12 \\x + 4 y + 6 z & = - 32 \\5 x + 3 y + 9 z & = 20\end{aligned}$$

A)no solution
B)(2, -7, -1)
C)(-8, -7, 9)
D)(8, -7, -2)

Question 58

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
$$\begin{array} { r } x + y + z = - 10 \\x - y + 5 z = - 24 \\3 x + y + z = - 14\end{array}$$

A)(-5, -3, -2)
B)(-2, -3, -5)
C)(-5, -2, -3)
D)no solution

Question 59

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
A deli sells three sizes of chicken sandwiches: the small chicken sandwich contains 4 ounces of meat and sells for $3.00; the regular chicken sandwich contains 8 ounces of meat and sells for $3.50; and the large chicken sandwich contains 10 ounces of meat and sells for $4.00. A customer requests a selection of each size for a reception. She and the manager agree on a combination of 52 sandwiches made from 22 pounds 4 ounces of chicken for a total cost of $178. How many of each size sandwich will be in this combination? (Note: 1 pound = 16 ounces)

A)24 small sandwiches, 10 medium sandwiches, 18 large sandwiches.
B)20 small sandwiches, 22 medium sandwiches, 10 large sandwiches.
C)22 small sandwiches, 16 medium sandwiches, 14 large sandwiches.
D)18 small sandwiches, 12 medium sandwiches, 22 large sandwiches.

Question 60

Solve the system of linear equations using the elimination method.
$$\begin{aligned}x + y + z & = 9 \\2 x - 3 y + 4 z & = 7 \\x - 4 y + 3 z & = - 2\end{aligned}$$

A) $\left( \frac { z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$
B) $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$
C) $\left( \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$
D) $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$

Question 61

Solve the problem.
A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 14 hours to paint, and 7 hours to fire. If the workshop has 86 hours for preparation time, 66 hours for painting, and 91 hours for firing, how many of each can be made?

A)4 wreaths, 3 trees, 6 sleighs
B)3 wreaths, 6 trees, 4 sleighs
C)7 wreaths, 5 trees, 4 sleighs
D)6 wreaths, 4 trees, 3 sleighs

Question 62

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z.
$$\frac { x } { ( x - 4 ) ( x - 5 ) }$$

A) $\frac { - 5 } { x - 4 } + \frac { 4 } { x - 5 }$
B) $\frac { 4 } { x - 4 } + \frac { - 5 } { x - 5 }$
C) $\frac { - 4 } { x - 4 } + \frac { 5 } { x - 5 }$
D) $\frac { - 4 } { x - 4 } + \frac { - 5 } { x - 5 }$

Question 63

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form.
$$\begin{aligned}x - y + 4 z & = 16 \\4 x + z & = 5 \\x + 5 y + z & = 25\end{aligned}$$

A)(0, 4, 5)
B)(5, 4, 0)
C)(0, 5, 4)
D)(5, 0, 4)

Question 64

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution.
$$\begin{array} { r } x + 3 y + 2 z = 11 \\4 y + 9 z = - 12 \\x + 7 y + 11 z = - 1\end{array}$$

A) $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } + 3 , \mathrm { z } \right)$
B) $\left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right)$
C) $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } - 3 , \mathrm { z } \right)$
D) $\left( - \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$

Question 65

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution.
$$\begin{array} { r r } x + y + z & = 9 \\2 x - 3 y + 4 z & = 7 \\x - 4 y + 3 z & = - 2\end{array}$$

A) $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$
B) $\left( \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$
C) $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$
D) $\left( \frac { z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$

Question 66

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution.
$$\begin{aligned}x + y + z & = 7 \\x - y + 2 z & = 7 \\2 x + 3 z & = 14\end{aligned}$$

A) $\left( - \frac { 3 z } { 2 } - 7,2 z , z \right)$
B) $\left( - \frac { 3 z } { 2 } + 7,2 z , z \right)$
C) $\left( - \frac { 3 z } { 2 } + 7 , \frac { z } { 2 } , z \right)$
D) $\left( - \frac { 3 z } { 2 } - 7 , \frac { z } { 2 } , z \right)$

Question 67

Solve the problem.
The Family Arts Center charges $23 for adults, $16 for senior citizens, and $6 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,492 for 862 tickets sold. There were 40 more children than adults. How many children attended?

A)300 children
B)451 children
C)330 children
D)222 children

Question 68

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z.
$$\begin{array} { r r } x + 8 y + 8 z = & 8 \\7 x + 7 y + z = & 1 \\8 x + 15 y + 9 z = & - 9\end{array}$$

A)no solution
B)(1, -1, 1)
C)(-1, 0, 1)
D)(0, 0, 1)

Question 69

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution.
$$\begin{array} { l } x + y + z = 7 \\x - y + 2 z = 7\end{array}$$

A) $( 8 , - 3,2 )$
В) $( - 3 z + 14,2 z - 7 , z )$
C) $( 4,1,2 )$
D) $\left( - \frac { 3 } { 2 } z + 7 , \frac { 1 } { 2 } z , z \right)$

Question 70

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution.
7x - y + 2z = 63 8x + 2z = 74 4y + z = 25

A)(7, 4, 9)
B)(-7, 4, 14)
C)(7, 9, 4)
D)(-7, 14, 4)

Question 71

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z.
$$\left[ \begin{array} { r r r | r } 1 & 0 & 0 & - 8 \\0 & 1 & 0 & 4 \\0 & 0 & 0 & - 9\end{array} \right]$$

A)dependent; (-8, 4)
B)inconsistent
C)dependent; (8, -4)
D)dependent; (-8, 4, -9)

Question 72

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution.
$$\left[ \begin{array} { l l l | l } 1 & 0 & - 5 & 3 \\0 & 1 & 9 & - 7 \\0 & 0 & 0 & 0\end{array} \right]$$

A) dependent; $( 3 , - 7 , - 5 )$
B) dependent; $( 3 + 5 z , y = - 7 - 9 z , z )$
C) dependent; $( 3 - 5 z , - 7 + 9 z , z )$
D) inconsistent

Question 73

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z.
$\frac { x - 17 } { ( x - 2 ) ( x - 5 ) }$

A) $\frac { 5 } { x - 2 } + \frac { 4 } { x - 5 }$
B) $\frac { - 4 } { x - 2 } + \frac { 5 } { x - 5 }$
C) $\frac { 5 } { x - 2 } + \frac { - 4 } { x - 5 }$
D) $\frac { 4 } { x - 2 } + \frac { - 5 } { x - 5 }$

Question 74

Solve the problem.
Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 136 g protein, 125 g fat, and 174 g carbohydrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal?

A)3 mushrooms, 9 meatballs, 5 eggs
B)10 mushrooms, 6 meatballs, 4 eggs
C)5 mushrooms, 3 meatballs, 9 eggs
D)9 mushrooms, 5 meatballs, 3 eggs

Question 75

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution.
$$\begin{array} { r r } 5 x + 2 y + z & = - 11 \\2 x - 3 y - z & = 17 \\7 x - y & = 12\end{array}$$

A) $( - 2,0 , - 1 )$
B) $( 1 , - 5,0 )$
C) no solution
D) $( 0 , - 6,1 )$

Question 76

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z.
$$\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & - 4\end{array} \right]$$

A)inconsistent
B)dependent; z = -4
C)dependent; (0, -4)
D)dependent; (0, 0)

Question 77

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution.
$$\begin{aligned}4 x - y + 3 z & = 12 \\x + 4 y + 6 z & = - 32 \\5 x + 3 y + 9 z & = 20\end{aligned}$$

A)(8, -7, -2)
B)(-8, -7, 9)
C)no solution
D)(2, -7, -1)

Question 78

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z.
Three shrimp boats supply the shrimp wholesalers on Hilton Head with fresh catch. The Annabelle takes 50% of its catch to Hudson's, 20% to Captain J's, and 30% to Mainstreet. The Curly Q takes 40% of its catch to Hudson's, 40% to Captain J's, and 20% to Mainstreet. The SloJoe takes 30% of its catch to Hudson's, 40% to Captain J's, and 30% to Mainstreet. One week Hudson's received 228.7 pounds of shrimp, Captain J's received 201.8 pounds, and Mainstreet received 151.5 pounds. How many pounds of shrimp did each boat catch?

A)Annabelle 196 lbs, Curly Q 231 lbs, SloJoe 155 lbs
B)Annabelle 196 lbs, Curly Q 155 lbs, SloJoe 231 lbs
C)Annabelle 231 lbs, Curly Q 196 lbs, SloJoe 155 lbs
D)Annabelle 155 lbs, Curly Q 231 lbs, SloJoe 196 lbs

Question 79

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution.
$$\begin{array} { l } x + y + z = 9 \\2 x - 3 y + 4 z = 7\end{array}$$

A) $\left( \frac { 27 } { 5 } , \frac { 13 } { 5 } , 1 \right)$
B) $\left( - \frac { 7 } { 5 } z + \frac { 34 } { 5 } , \frac { 2 } { 5 } z + \frac { 11 } { 5 } , z \right)$
C) no solution
D) $\left( \frac { 3 } { 5 } z + \frac { 16 } { 5 } , - \frac { 8 } { 5 } z + \frac { 29 } { 5 } , z \right)$

Question 80

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution.
$$\begin{array} { l } 5 x - y + z = 8 \\7 x + y + z = 6\end{array}$$

A) no solution
B) $( - z + 3,4 z + 7 , z )$
C) $\left( \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z , z \right)$
D) $\left( - \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z - \frac { 13 } { 6 } , z \right)$