# College Algebra (Open Stax)

## Educators

MB
SM

### Problem 1

Can a system of linear equations have exactly two solutions? Explain why or why not.

Tony W.

### Problem 2

If you are performing a break-even analysis for a business and their cost and revenue equations are dependent, explain what this means for the company's profit margins.

MB
Matt B.

### Problem 3

If you are solving a break-even analysis and get a negative break-even point, explain what this
signifies for the company?

Tony W.

### Problem 4

If you are solving a break-even analysis and there is no break-even point, explain what this means
for the company. How should they ensure there is a break-even point?

MB
Matt B.

### Problem 5

Given a system of equations, explain at least two different methods of solving that system.

Tony W.

### Problem 6

For the following exercises, determine whether the given ordered pair is a solution to the system of equations.
$$\begin{array}{l}{5 x-y=4} \\ {x+6 y=2 \text { and }(4,0)}\end{array}$$

MB
Matt B.

### Problem 7

For the following exercises, determine whether the given ordered pair is a solution to the system of equations
$$\begin{array}{l}{-3 x-5 y=13} \\ {-x+4 y=10 \text { and }(-6,1)}\end{array}$$

Tony W.

### Problem 8

For the following exercises, determine whether the given ordered pair is a solution to the system of equations
$$\begin{array}{l}{3 x+7 y=1} \\ {2 x+4 y=0 \text { and }(2,3)}\end{array}$$

MB
Matt B.

### Problem 9

For the following exercises, determine whether the given ordered pair is a solution to the system of equations
\begin{aligned}-2 x+5 y &=7 \\ 2 x+9 y &=7 \text { and }(-1,1) \end{aligned}

Tony W.

### Problem 10

For the following exercises, determine whether the given ordered pair is a solution to the system of equations
\begin{aligned} x+8 y &=43 \\ 3 x-2 y &=-1 \text { and }(3,5) \end{aligned}

MB
Matt B.

### Problem 11

For the following exercises, solve each system by substitution.
\begin{aligned} x+3 y &=5 \\ 2 x+3 y &=4 \end{aligned}

Tony W.

### Problem 12

For the following exercises, solve each system by substitution.
$$\begin{array}{c}{3 x-2 y=18} \\ {5 x+10 y=-10}\end{array}$$

MB
Matt B.

### Problem 13

For the following exercises, solve each system by substitution.
$$\begin{array}{l}{4 x+2 y=-10} \\ {3 x+9 y=0}\end{array}$$

Tony W.

### Problem 14

For the following exercises, solve each system by substitution.
$$\begin{array}{l}{2 x+4 y=-3.8} \\ {9 x-5 y=1.3}\end{array}$$

MB
Matt B.

### Problem 15

For the following exercises, solve each system by substitution.
$$\begin{array}{l}{-2 x+3 y=1.2} \\ {-3 x-6 y=1.8}\end{array}$$

Tony W.

### Problem 16

For the following exercises, solve each system by substitution.
\begin{aligned} x-0.2 y &=1 \\-10 x+2 y &=5 \end{aligned}

MB
Matt B.

### Problem 17

For the following exercises, solve each system by substitution.
$$\begin{array}{l}{3 \quad x+5 y=9} \\ {30 x+50 y=-90}\end{array}$$

Tony W.

### Problem 18

For the following exercises, solve each system by substitution.
$$\begin{array}{l}{-3 x+y=2} \\ {12 x-4 y=-8}\end{array}$$

MB
Matt B.

### Problem 19

For the following exercises, solve each system by substitution.
$$\begin{array}{l}{\frac{1}{2} x+\frac{1}{3} y=16} \\ {\frac{1}{6} x+\frac{1}{4} y=9}\end{array}$$

Tony W.

### Problem 20

For the following exercises, solve each system by substitution.
$$\begin{array}{l}{-\frac{1}{4} x+\frac{3}{2} y=11} \\ {-\frac{1}{8} x+\frac{1}{3} y=3}\end{array}$$

MB
Matt B.

### Problem 21

For the following exercises, solve each system by addition.
\begin{aligned}-2 x+5 y &=-42 \\ 7 x+2 y &=30 \end{aligned}

Tony W.

### Problem 22

For the following exercises, solve each system by addition.
$$\begin{array}{l}{6 x-5 y=-34} \\ {2 x+6 y=4}\end{array}$$

MB
Matt B.

### Problem 23

For the following exercises, solve each system by addition.
\begin{aligned} 5 x-y &=-2.6 \\-4 x-6 y &=1.4 \end{aligned}

Tony W.

### Problem 24

For the following exercises, solve each system by addition.
$$\begin{array}{l}{7 x-2 y=3} \\ {4 x+5 y=3.25}\end{array}$$

MB
Matt B.

### Problem 25

For the following exercises, solve each system by addition.
$$\begin{array}{l}{-x+2 y=-1} \\ {5 x-10 y=6}\end{array}$$

Tony W.

### Problem 26

For the following exercises, solve each system by addition.
\begin{aligned} 7 x+6 y &=2 \\-28 x-24 y &=-8 \end{aligned}

MB
Matt B.

### Problem 27

For the following exercises, solve each system by substitution.
$$\begin{array}{l}{\frac{5}{6} x+\frac{1}{4} y=0} \\ {\frac{1}{8} x-\frac{1}{2} y=-\frac{43}{120}}\end{array}$$

Tony W.

### Problem 28

For the following exercises, solve each system by addition.
\begin{aligned} \frac{1}{3} x+\frac{1}{9} y &=\frac{2}{9} \\-\frac{1}{2} x+\frac{4}{5} y &=-\frac{1}{3} \end{aligned}

MB
Matt B.

### Problem 29

For the following exercises, solve each system by addition.
\begin{aligned}-0.2 x+0.4 y &=0.6 \\ x-2 y &=-3 \end{aligned}

Tony W.

### Problem 30

For the following exercises, solve each system by addition.
\begin{aligned}-0.1 x+0.2 y &=0.6 \\ 5 x-10 y &=1 \end{aligned}

MB
Matt B.

### Problem 31

For the following exercises, solve each system by any method.
\begin{aligned} 5 x+9 y &=16 \\ x+2 y &=4 \end{aligned}

Tony W.

### Problem 32

For the following exercises, solve each system by any method.
$$\begin{array}{l}{6 x-8 y=-0.6} \\ {3 x+2 y=0.9}\end{array}$$

MB
Matt B.

### Problem 33

For the following exercises, solve each system by any method.
$$\begin{array}{l}{5 x-2 y=2.25} \\ {7 x-4 y=3}\end{array}$$

Tony W.

### Problem 34

For the following exercises, solve each system by any method.
\begin{aligned} x-\frac{5}{12} y &=-\frac{55}{12} \\-6 x+\frac{5}{2} y &=\frac{55}{2} \end{aligned}

MB
Matt B.

### Problem 35

For the following exercises, solve each system by any method.
$$\begin{array}{l}{7 x-4 y=\frac{7}{6}} \\ {2 x+4 y=\frac{1}{3}}\end{array}$$

Tony W.

### Problem 36

For the following exercises, solve each system by any method.
$$\begin{array}{l}{3 x+6 y=11} \\ {2 x+4 y=9}\end{array}$$

MB
Matt B.

### Problem 37

For the following exercises, solve each system by any method.
\begin{aligned} \frac{7}{3} x-\frac{1}{6} y &=2 \\-\frac{21}{6} x+\frac{3}{12} y &=-3 \end{aligned}

Tony W.

### Problem 38

For the following exercises, solve each system by any method.
$$\begin{array}{l}{\frac{1}{2} x+\frac{1}{3} y=\frac{1}{3}} \\ {\frac{3}{2} x+\frac{1}{4} y=-\frac{1}{8}}\end{array}$$

MB
Matt B.

### Problem 39

For the following exercises, solve each system by any method.
$$\begin{array}{l}{2.2 x+1.3 y=-0.1} \\ {4.2 x+4.2 y=2.1}\end{array}$$

Tony W.

### Problem 40

For the following exercises, solve each system by any method.
\begin{aligned} 0.1 x+0.2 y &=2 \\ 0.35 x-0.3 y &=0 \end{aligned}

MB
Matt B.

### Problem 41

For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions.
$$\begin{array}{l}{3 x-y=0.6} \\ {x-2 y=1.3}\end{array}$$

Tony W.

### Problem 42

For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions.
$$\begin{array}{l}{-x+2 y=4} \\ {2 x-4 y=1}\end{array}$$

MB
Matt B.

### Problem 43

For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions.
\begin{aligned} x+2 y &=7 \\ 2 x+6 y &=12 \end{aligned}

Tony W.

### Problem 44

For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions.
\begin{aligned} 3 x-5 y &=7 \\ x-2 y &=3 \end{aligned}

MB
Matt B.

### Problem 45

For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions.
\begin{aligned} 3 x-2 y &=5 \\-9 x+6 y &=-15 \end{aligned}

Tony W.

### Problem 46

For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth.
\begin{aligned} 0.1 x+0.2 y &=0.3 \\-0.3 x+0.5 y &=1 \end{aligned}

MB
Matt B.

### Problem 47

For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth.
\begin{aligned}-0.01 x+0.12 y &=0.62 \\ 0.15 x+0.20 y &=0.52 \end{aligned}

Tony W.

### Problem 48

For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth.
\begin{aligned} 0.5 x+0.3 y &=4 \\ 0.25 x-0.9 y &=0.46 \end{aligned}

MB
Matt B.

### Problem 49

For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth.
\begin{aligned} 0.15 x+0.27 y &=0.39 \\-0.34 x+0.56 y &=1.8 \end{aligned}

Tony W.

### Problem 50

For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth.
\begin{aligned}-0.71 x+0.92 y &=0.13 \\ 0.83 x+0.05 y &=2.1 \end{aligned}

MB
Matt B.

### Problem 51

For the following exercises, solve each system in terms of $A, B, C, D, E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A \neq B$ and $A E \neq B D .$
$$\begin{array}{l}{x+y=A} \\ {x-y=B}\end{array}$$

Tony W.

### Problem 52

For the following exercises, solve each system in terms of $A, B, C, D, E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A \neq B$ and $A E \neq B D .$
$$\begin{array}{l}{x+A y=1} \\ {x+B y=1}\end{array}$$

MB
Matt B.

### Problem 53

For the following exercises, solve each system in terms of $A, B, C, D, E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A \neq B$ and $A E \neq B D .$
$$\begin{array}{l}{A x+y=0} \\ {B x+y=1}\end{array}$$

Tony W.

### Problem 54

For the following exercises, solve each system in terms of $A, B, C, D, E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A \neq B$ and $A E \neq B D .$
$$\begin{array}{r}{A x+B y=C} \\ {x+y=1}\end{array}$$

MB
Matt B.

### Problem 55

For the following exercises, solve each system in terms of $A, B, C, D, E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A \neq B$ and $A E \neq B D .$
$$\begin{array}{l}{A x+B y=C} \\ {D x+E y=F}\end{array}$$

Tony W.

### Problem 56

For the following exercises, solve for the desired quantity.
A stuffed animal business has a total cost of production $C=12 x+30$ and a revenue function $R=20 x .$ Find the break-even point.

MB
Matt B.

### Problem 57

For the following exercises, solve for the desired quantity.
A fast-food restaurant has a cost of production $C(x)=11 x+120$ and a revenue function $R(x)=5 x$ . When does the company start to turn a profit?

Tony W.

### Problem 58

For the following exercises, solve for the desired quantity.
A cell phone factory has a cost of production $C(x)=150 x+10,000$ and a revenue function $R(x)=200 x .$ What is the break-even point?

MB
Matt B.

### Problem 59

For the following exercises, solve for the desired quantity.

Tony W.

### Problem 64

For the following exercises, use a system of linear equations with two variables and two equations to solve.

MB
Matt B.

### Problem 71

For the following exercises, use a system of linear equations with two variables and two equations to solve.

MB
Matt B.

### Problem 75

For the following exercises, use a system of linear equations with two variables and two equations to solve.
A store clerk sold 60 pairs of sneakers. The high-tops sold for $\$ 98.99$and the low-tops sold for$\$129.99 .$ If the receipts for the two types of sales totaled $\$ 6,404.40$, how many of each type of sneaker were sold? Tony W. Numerade Educator ### Problem 76 For the following exercises, use a system of linear equations with two variables and two equations to solve. A concert manager counted 350 ticket receipts the day after a concert. The price for a student ticket was$\$12.50$ , and the price for an adult ticket was $\$ 16.00$. The register confirms that$\$5,075$ was taken in. How many student tickets and adult tickets were sold?

MB
Matt B.
Admission into an amusement park for 4 children and 2 adults is $\$ 116.90 .$For 6 children and 3 adults, the admission is$\$175.35$ . Assuming a different price for children and adults, what is the price of the child's ticket and the price of the adult ticket?