Deck 10: Systems of Equations and Inequalities

Question 1

State whether the equation is linear.

Answer 1

not linear

Question 2

Graph each linear system, either by hand or using a graphing device. Use the graph to determine whether the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it.

Answer 2

one solution :

Question 3

State whether the equation is linear.

Answer 3

linear.

Question 4

Graph each linear system, either by hand or using a graphing device. Use the graph to determine whether the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it.

Question 5

Solve the system.

Question 6

State whether the system of equations is linear.

Question 7

A boat travels upstream (against the current) between two points on a river mi apart in hours. The return trip downstream takes only minutes. What is the boat's speed, and how fast does the current in the river flow?

Question 8

A money manager invests his client's savings into two accounts, one paying and the other simple interest per year. He puts three times as much in the lower yielding investment because it's less risky than the other one. His client's annual interest is . How much did he invest at each rate?

Question 9

Solve the system.

Question 10

State whether the equation is linear.

Question 11

Solve the system.

Question 12

Graph each linear system, either by hand or using a graphing device. Use the graph to determine whether the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it.

Question 13

Solve the system.

Question 14

Solve the system.

Question 15

Solve the system.

Question 16

Solve the system.

Question 17

There are 63 coins in Taylor's pocket, all in quarters and dimes. The total value is $9.60. Find the number of each type of coin.

Question 18

The sum of the digits of a two digit number is 10. When the digits are interchanged, the number is decreased by . Find the number.

Question 19

A man invests a total of in two accounts, one paying simple interest per year and the other paying simple interest per year. His annual interest from both accounts is , . How much did he invest at each rate?

Question 20

Solve the system.

Question 21

Find the complete solution of the linear system or show that it is inconsistent.

Question 22

Find the quadratic polynomial whose graph passes through the points , , and .

Question 23

Find the complete solution of the linear system or show that it is inconsistent.

Question 24

Find the complete solution of the linear system or show that it is inconsistent.

Question 25

Use back-substitution to solve the triangular system.

Question 26

Use back-substitution to solve the triangular system.

Question 27

Find the complete solution of the linear system or show that it is inconsistent.

Question 28

State whether the system of equations is linear.

Question 29

Determine whether the matrix is in echelon or reduced echelon form. Write the corresponding system of equations.

Question 30

Find the complete solution of the linear system or show that it is inconsistent.

Question 31

Find the complete solution of the linear system or show that it is inconsistent.

Question 32

Find the complete solution of the linear system or show that it is inconsistent.

Question 33

Use back-substitution to solve the triangular system.

Question 34

Determine whether the matrix is in echelon or reduced echelon form. Write the corresponding system of equations.

Question 35

Find the complete solution of the linear system or show that it is inconsistent.

Question 36

Find the complete solution of the linear system or show that it is inconsistent.

Question 37

Find the quadratic polynomial whose graph passes through the points , , and .

Question 38

Find the complete solution of the linear system or show that it is inconsistent.

Question 39

Determine whether the matrix is in echelon or reduced echelon form. Write the corresponding system of equations.

Question 40

A money manager invests of her client's money into three types of funds. It's estimated that Fund A will return over the next year, Fund B , and Fund C . She decides to invest equal amounts in Fund A and Fund B and her client hopes to get a annual return. How much should she invest at each rate?

Question 41

Given , find , or explain why the operation cannot be performed.

Question 42

Solve the system of linear equations.

Question 43

Given and , find , or explain why the operation cannot be performed.

Question 44

Dana, Susan, and Caitlin enter a race in which they have to run, swim, and cycle over a marked course. Their average speeds are given in the table. Caitlin finishes first with a total time of 2 h 45 min. Dana comes in second with a time of 3 h 30 min. Susan finishes last with a time of 4 h 15 min. Find the distance (in miles) for each part of the race.
Average speed (mi/h)
Running
Swimming
Cycling
Dana
10
4
20
Susan
5
4
20
Caitlin
10
3
40

Question 45

Solve the system of linear equations.

Question 46

Given and , find , or explain why the operation cannot be performed.

Question 47

Solve the system of linear equations.

Question 48

Solve the system of linear equations.

Question 49

Solve the system of linear equations.

Question 50

Solve the system of linear equations.

Question 51

Solve the system of linear equations.

Question 52

Given and , find , or explain why the operation cannot be performed.

Question 53

Solve the system of linear equations.

Question 54

Solve the system of linear equations.

Question 55

Given and , find , or explain why the operation cannot be performed.

Question 56

Solve the system of linear equations.

Question 57

Given and , find , or explain why the operation cannot be performed.

Question 58

Solve the system of linear equations.

Question 59

Given and , find , or explain why the operation cannot be performed.

Question 60

Given and , find , or explain why the operation cannot be performed.

Question 61

Given and , solve , for , or explain why there is no solution.

Question 62

Given , , find , or explain why the operation cannot be performed.

Question 63

Solve the system of equations by converting to a matrix equation and using its inverse coefficient matrix .

Question 64

Find the inverse of the matrix , if it exists.

Question 65

Find the inverse of the matrix, if it exists.

Question 66

Find , or explain why the operation cannot be performed.

Question 67

Given , and , determine which of , , , , and are defined, and calculate them.

Question 68

Solve the system of equations by converting to a matrix equation and using its inverse coefficient matrix .

Question 69

Find the inverse of the matrix , if it exists.

Question 70

Given and , find , or explain why the operation cannot be performed.

Question 71

Find the inverse of the matrix , if it exists.

Question 72

Find the inverse of the matrix , if it exists.

Question 73

Solve for and .

Question 74

Find the inverse of the matrix, if it exists.

Question 75

Given and , solve , for the matrix , or explain why there is no solution.

Question 76

Find the inverse of the matrix , if it exists.

Question 77

Solve for and .

Question 78

Given and , solve , for the matrix , or explain why there is no solution.

Question 79

Write the system of equations in matrix form.

Question 80

Given and , find , or explain why the operation cannot be performed.