Deck 7: Section 1: Systems of Linear Equations

Question 1

Solve the system of equations.
-x + y - z = 8
4x - 2y + 5z = -28
2x - 2y + 2z = -14

A) {(0, 4, -4)}
B) { $\varnothing$ }
C) {(x, y, z) | -x + y - z = 8}
D) {(x, y, z) | 4x - 2y + 5z = -28}

Answer 1

{ $\varnothing$ }

Question 2

For Monday morning's staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $11.50 (excluding sales tax). For Friday's meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $13.00 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?

A) $1.75 per bag for bagels, $2.75 per package for cream cheese
B) $3.25 per bag for bagels, $2.50 per package for cream cheese
C) $2.00 per bag for bagels, $2.50 per package for cream cheese
D) $2.50 per bag for bagels, $2.00 per package for cream cheese

Answer 2

$2.00 per bag for bagels, $2.50 per package for cream cheese

Question 3

Solve the system of equations.
2x - 3y + z = 4
8x - 12y + 4z = 16
-4x + 6y - 2z = -8

A) {(-3, 6, 7)}
B) {(-4, -2, -1)}
C) { $\varnothing$ }
D) {(x, y, z) | 2x - 3y + z = 4}

Answer 3

{(x, y, z) | 2x - 3y + z = 4}

Question 4

Solve the system of equations. -3x + 3y - 4z = -58
5x + 2y - z = 1
-4x - 3y + 3z = 23

A) {(4, -4, 2)}
B) {(1, -6, 7)}
C) {(4, -6, 7)}
D) {(-6, 6, 5)}

Question 5

When the graphs of two independent linear equations (each in three variables) intersect, the intersection is

A) a line.
B) a plane.
C) a point.
D) None of these.

Question 6

Solve the system of equations. 0.5x + 2y = 1.25
-0)875x + 1.5y = 2.8125

A) {(-1, 1.5)}
B) {(0, 1)}
C) {(0, 3)}
D) {(-1.5, 1)}

Question 7

Suzanne invested $18,100 in two mutual fund accounts: the Abernathy Fund and the Brice Fund. During the subsequent year, The Abernathy Fund earned 11% and the Brice account earned 6%. At the end of the year, the total interest earned was $1,391. How much did Suzanne invest in each fund?

A) $6,600 in the Abernathy Fund, $11,500 in the Brice Fund
B) $5,100 in the Abernathy Fund, $13,000 in the Brice Fund
C) $6,100 in the Abernathy Fund, $12,000 in the Brice Fund
D) $6,600 in the Abernathy Fund, $11,700 in the Brice Fund

Question 8

When rolling a pair of dice, the probability of getting a particular total is not very high. For example, the probability of failing to roll a total of 7 is 5 times the probability of successfully rolling a total of 7. The total probability (probability of failing to roll a 7 + probability of successfully rolling a 7) is 1. What is the probability of rolling a 7?

A) 1 in 6
B) 1 in 18
C) 1 in 9
D) None of these.

Question 9

Solve the system of linear equations by the substitution method.

A)

B)

C) No solution. The system is inconsistent.
D)

Question 10

Solve the system of linear equations.

A) No solution. The system is inconsistent.
B) {(1, 5)}
C) {(3, 7)}
D) {(-3, -6)}

Question 11

Solve the system of equations.

A) {(-1, 2, -2)}
B) {(-1, 0, 3)}
C) {(-4, 0, 3)}
D) {(0, 1, 1)}

Question 12

For the system find the value of a so that the solution set to the system is {(7, 3)}.

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

Question 13

Solve the system of linear equations by the substitution method. 8x = -3y - 15
5x - 8y = 40

A) {(-2, -4)}
B) {(0, -5)}
C) No solution. The system is inconsistent.
D) {(2, -2)}

Question 14

Which of the following graphs correctly describes the system and its solution?

A)

B)

C)

D)
None of these.

Question 15

Fred, Tiger, and Nancy play a round of golf together. Their combined score is 224. Fred's score was 4 more than Tiger's, and Nancy's score was 6 more than Fred's. What was each person's score?

A) Fred = 74 ; Tiger = 70 ; Nancy = 80
B) Fred = 71 ; Tiger = 67 ; Nancy = 77
C) Fred = 76 ; Tiger = 72 ; Nancy = 82
D) Fred = 70 ; Tiger = 74 ; Nancy = 80

Question 16

Cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 20 pounds of a mixture that sells for $4.25 per pound?

A) 13 lb cashews, 7 lb peanuts
B) 16 lb cashews, 4 lb peanuts
C) 17 lb cashews, 3 lb peanuts
D) 15 lb cashews, 5 lb peanuts

Question 17

When three linear equations (each in three variables) are graphed, two of the equations are seen to be parallel planes. The system is

A) normal.
B) incomplete.
C) inconsistent.
D) dependent.