Algebra 2

Educators

KB
AG

Problem 1

$$\left\{\begin{array}{l}{y=x-2} \\ {y=-2 x+7}\end{array}\right.$$

KB
Karan B.

Problem 2

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

AG
Ankit G.

Problem 3

\left\{\begin{aligned} 2 x+4 y &=12 \\ x+y &=2 \end{aligned}\right.

AG
Ankit G.

Problem 4

$$\left\{\begin{array}{l}{x=-3} \\ {y=5}\end{array}\right.$$

AG
Ankit G.

Problem 5

$$\left\{\begin{array}{l}{2 x-2 y=4} \\ {y-x=6}\end{array}\right.$$

AG
Ankit G.

Problem 6

$$\left\{\begin{array}{c}{3 x+y=5} \\ {x-y=7}\end{array}\right.$$

AG
Ankit G.

Problem 7

\left\{\begin{aligned}-5 x+y &=-9 \\ x+3 y &=21 \end{aligned}\right.

KB
Karan B.

Problem 8

$$\left\{\begin{array}{l}{y=x} \\ {y-5 x=0}\end{array}\right.$$

AG
Ankit G.

Problem 9

$$\left\{\begin{array}{l}{x=10} \\ {x=y-10}\end{array}\right.$$

KB
Karan B.

Problem 10

For Exercises $10-11,$ use your graphing calculator. Find linear models for each set of data. Use each model to predict the year in which the quantities will be equal.
Annual U.S. Consumption of Vegetables
(PICTURE NOT COPY)

Weston B.

Problem 11

For Exercises $10-11,$ use your graphing calculator. Find linear models for each set of data. Use each model to predict the year in which the quantities will be equal.
U.S. Life Expectancy at Birth
(PICTURE NOT COPY)

KB
Karan B.

Problem 12

a. Business The spreadsheet shows the monthly revenue and monthly expenses for a new business. Find a linear model for monthly revenue and a linear model for monthly expenses.
b. Use the models to predict the month in which revenue will equal expenses.

Weston B.

Problem 13

Without graphing, classify each system as independent, dependent, or inconsistent.
\left\{\begin{aligned} 7 x-y &=6 \\-7 x+y &=-6 \end{aligned}\right.

KB
Karan B.

Problem 14

Without graphing, classify each system as independent, dependent, or inconsistent.
\left\{\begin{aligned}-3 x+y &=4 \\ x-\frac{1}{3} y &=1 \end{aligned}\right.

Weston B.

Problem 15

Without graphing, classify each system as independent, dependent, or inconsistent.
\left\{\begin{aligned} 4 x+8 y &=12 \\ x+2 y &=-3 \end{aligned}\right.

KB
Karan B.

Problem 16

Without graphing, classify each system as independent, dependent, or inconsistent.
$$\left\{\begin{array}{l}{y=2 x-1} \\ {y=-2 x+5}\end{array}\right.$$

Weston B.

Problem 17

Without graphing, classify each system as independent, dependent, or inconsistent.
$$\left\{\begin{array}{l}{x=6} \\ {x=-2}\end{array}\right.$$

AG
Ankit G.

Problem 18

Without graphing, classify each system as independent, dependent, or inconsistent.
$$\left\{\begin{array}{l}{2 y=5 x+6} \\ {-10 x+4 y=8}\end{array}\right.$$

AG
Ankit G.

Problem 19

Without graphing, classify each system as independent, dependent, or inconsistent.
\left\{\begin{aligned} x-3 y &=2 \\ 4 x-12 y &=8 \end{aligned}\right.

KB
Karan B.

Problem 20

Without graphing, classify each system as independent, dependent, or inconsistent.
$$\left\{\begin{array}{l}{x+4 y=12} \\ {2 x-8 y=4}\end{array}\right.$$

Weston B.

Problem 21

Without graphing, classify each system as independent, dependent, or inconsistent.
$$\left\{\begin{array}{l}{4 x+8 y=-6} \\ {6 x+12 y=-9}\end{array}\right.$$

KB
Karan B.

Problem 22

Without graphing, classify each system as independent, dependent, or inconsistent.
$$\left\{\begin{array}{l}{4 y-2 x=6} \\ {8 y=4 x-12}\end{array}\right.$$

Weston B.

Problem 23

Without graphing, classify each system as independent, dependent, or inconsistent.
$$\left\{\begin{array}{l}{y-x=0} \\ {y=-x}\end{array}\right.$$

KB
Karan B.

Problem 24

Without graphing, classify each system as independent, dependent, or inconsistent.
$$\left\{\begin{array}{l}{2 y-x=4} \\ {\frac{1}{2} x-y=2}\end{array}\right.$$

Weston B.

Problem 25

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{3=4 y+x} \\ {4 y=-x+3}\end{array}\right.$$

KB
Karan B.

Problem 26

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{x-2 y+1=0} \\ {x+4 y-6=0}\end{array}\right.$$

AG
Ankit G.

Problem 27

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{3 x+6 y-12=0} \\ {x+2 y=8}\end{array}\right.$$

KB
Karan B.

Problem 28

Graph and solve each system. Where necessary, estimate the solution.
\left\{\begin{aligned}-x+3 y &=6 \\ 2 x-y &=8 \end{aligned}\right.

Weston B.

Problem 29

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{3 x+y=3} \\ {2 x-y=7}\end{array}\right.$$

AG
Ankit G.

Problem 30

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{2 x+3 y=6} \\ {4 x=6 y+3}\end{array}\right.$$

AG
Ankit G.

Problem 31

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{10-3 x=-3 y} \\ {2=2 x+y}\end{array}\right.$$

AG
Ankit G.

Problem 32

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{3 x=-5 y+4} \\ {250+150 x=300}\end{array}\right.$$

Weston B.

Problem 33

Graph and solve each system. Where necessary, estimate the solution.
\left\{\begin{aligned} x+3 y &=6 \\ 6 y+2 x &=12 \end{aligned}\right.

KB
Karan B.

Problem 34

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{2 y+x=8} \\ {y-2 x=-6}\end{array}\right.$$

Weston B.

Problem 35

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{y=-2 x+6} \\ {x-3 y=-6}\end{array}\right.$$

KB
Karan B.

Problem 36

Graph and solve each system. Where necessary, estimate the solution.
$$\left\{\begin{array}{l}{-x-2=-2 y} \\ {2 x-4 y-4=0}\end{array}\right.$$

Weston B.

Banking To pay your monthly bills, you can either open a checking account or use an online banking service. A local bank charges $\$ 3$per month and$\$.40$ per check, while an online services charges a flat fee of $\$ 9$per month. a. Write and graph a system of linear equations to model the cost$c$of each service for$b$bills that you need to pay monthly. b. Find the point of intersection of the two linear models. What does this answer represent? c. If you pay about 12 bills per month, which service should you choose? Explain. KB Karan B. Numerade Educator Problem 38 Classify each system without graphing. $$\left\{\begin{array}{l}{3 x-2 y=8} \\ {4 y=6 x-5}\end{array}\right.$$ Weston B. Numerade Educator Problem 39 Classify each system without graphing. $$\left\{\begin{array}{l}{2 x+8 y=6} \\ {x=-4 y+3}\end{array}\right.$$ KB Karan B. Numerade Educator Problem 40 Classify each system without graphing. $$\left\{\begin{array}{l}{3 a+6 b=14} \\ {-a+2 b=3}\end{array}\right.$$ Weston B. Numerade Educator Problem 41 Classify each system without graphing. $$\left\{\begin{array}{l}{3 m=-5 n+4} \\ {n-\frac{6}{5}=-\frac{3}{5} m}\end{array}\right.$$ KB Karan B. Numerade Educator Problem 42 Classify each system without graphing. $$\left\{\begin{array}{l}{-12 x+4 y=8} \\ {y-4=3 x}\end{array}\right.$$ Weston B. Numerade Educator Problem 43 Classify each system without graphing. $$\left\{\begin{array}{l}{-6 y+18=12 x} \\ {3 y+6 x=9}\end{array}\right.$$ KB Karan B. Numerade Educator Problem 44 Fees Suppose you are going on vacation and leaving your dog in a kennel.The Bowowery charges$\$5$ per day, which includes a one-time grooming treatment. The Poochpad charges $\$ 20$per day and a one-time fee of$\$30$ for grooming.
a. Write a system of equations to represent the cost $c$ for $d$ days that your dog will stay at a kennel.
b. Using a graphing calculator, find the number of days for which the costs are the same.
c. If your vacation is a week long, which kennel should you choose? Explain.

Weston B.

Problem 45

Advertising You and your business partner are mailing advertising flyers to your customers. You address 6 flyers each minute and have already done $80 .$ Your partner addresses 4 flyers each minute and has already done $100 .$ Graph and solve a system of equations to find when the two of you will have

KB
Karan B.

Problem 46

Open-Ended Write a second equation for each system so that the system will have the indicated number of solutions.
$$\begin{array}{l}{\text { one }} \\ {\left\{\begin{array}{l}{y=-3 x+2} \\ {?}\end{array}\right.}\end{array}$$

Weston B.

Problem 47

Open-Ended Write a second equation for each system so that the system will have the indicated number of solutions.
$$\begin{array}{l}{\text { none }} \\ {\left\{\begin{array}{c}{y=-4 x-6} \\ {?}\end{array}\right.}\end{array}$$

KB
Karan B.

Problem 48

Open-Ended Write a second equation for each system so that the system will have the indicated number of solutions.
$$\begin{array}{l}{\text { an infinite number }} \\ {\left\{\begin{array}{c}{3 y=6 x+7} \\ {?}\end{array}\right.}\end{array}$$

Weston B.

Problem 49

Reasoning Is it possible for an inconsistent linear system to consist of two lines with the same $y$ -intercept? Explain.

KB
Karan B.

Problem 50

Writing Summarize the possible relationships for the $y$ -intercepts, slopes, and number of solutions in a system of two linear equations of two variables.

Weston B.

Problem 51

Open-Ended Write a second equation for each system so that the system will have the indicated number of solutions.
$$\begin{array}{l}{\text { infinite number of solutions }} \\ {\left\{\frac{x}{4}+\frac{y}{3}=1\right.} \\ {\text { ? }}\end{array}$$

KB
Karan B.

Problem 52

Open-Ended Write a second equation for each system so that the system will have the indicated number of solutions.
$$\begin{array}{l}{\text { no solutions }} \\ {\left\{\begin{array}{c}{5 x+2 y=10} \\ {?}\end{array}\right.}\end{array}$$

Weston B.

Problem 53

Write a system of linear equations with the solution set $\{(x, y) | y=5 x+2\}$

KB
Karan B.

Problem 54

Critical Thinking Look back through the exercises on the previous two pages to find several dependent systems. What relationship exists between the equations in each system?

Weston B.

Problem 55

Economics Resarch shows that in a certain market only 2000 widgets can be sold at $\$ 8$each, but if the price is reduced to$\$3,$ then $10,000$ can be sold.
a. Let $p$ represent price and $n$ represent the number of widgets. Identify the independent variable and the dependent variable.
b. Use the information above to write a linear demand equation.
c. A shop can make 2000 widgets for $\$ 5$each and$20,000$widgets for$\$2$ each. Use this information to write a linear supply equation.
d. Find the equilibrium point where supply is equal to demand and profit is a maximum. Explain the meaning of the coordinates of this point within the context of the exercise.

KB
Karan B.

Problem 56

Which is an equation for Line 2$?$
$$\begin{array}{ll}{\text { A. } 3 x-5 y=15} & {\text { B. } 3 x+5 y=3} \\ {\text { C. } 3 x+5 y=15} & {\text { D. } 5 x+3 y=15}\end{array}$$

Weston B.

Problem 57

Which is NOT an equation for Line 1$?$
$$\begin{array}{ll}{\text { F. } y=x} & {\text { G. } x+y=0} \\ {\text { H. } x-y=0} & {\text { J. } y-x=0}\end{array}$$

KB
Karan B.

Problem 58

Which point lies on both Line 1 and Line 2$?$
$$\begin{array}{ll}{\text { A. }(0,0)} & {\text { B. }(1.875,1.875)} \\ {\text { C. }(1.95,1.95)} & {\text { D. }(2,2)}\end{array}$$

Weston B.

Problem 59

What is the solution of the system? $\left\{\begin{array}{c}{5 x+6 y=-24} \\ {-2 x+3 y=15} \\ {\text { H. }(-6,1)}\end{array}\right.$
$$\begin{array}{llll}{\text { F. }(6,-1)} & {\text { G. }(6,1)} & {\text { H. }(-6,1)} & {\text { J. }(-6,-1)}\end{array}$$

KB
Karan B.

Problem 60

Explain how you can use slopes to show that the system $\left\{\begin{array}{l}{2 x-5 y=23} \\ {3 y-7 x=-8}\end{array}\right.$ is NOT inconsistent.

Weston B.

Problem 61

One equation of a system of equations is $2 x-3 y=5$
a. Find a second equation such that the system is dependent.
b. Find a second equation such that the system is inconsistent.

KB
Karan B.

Problem 62

Graph each inequality on a coordinate plane.
$$3 x-4 y \geq 16$$

Weston B.

Problem 63

Graph each inequality on a coordinate plane.
$$-5 x>8 y+4$$

KB
Karan B.

Problem 64

Graph each inequality on a coordinate plane.
$$x<-4$$

Weston B.

Problem 65

Write an equation for each line.
$$m=-\frac{2}{3} ; \text { contains }(-9,4)$$

KB
Karan B.

Problem 66

Write an equation for each line.
$$m=0 ; \text { contains }(3,4)$$

Weston B.

Problem 67

Write an equation for each line.
$$m=2 ; \text { contains }(-2,-3)$$

KB
Karan B.

Problem 68

Write an equation for each line.
$$m=-\frac{1}{2} ; \text { contains }(2,-6)$$

Weston B.

Problem 69

Solve each equation and check the solution.
$$3 n=-4(2+n)$$

KB
Karan B.

Problem 70

Solve each equation and check the solution.
$$-4 a+a=7 a-6$$

Weston B.

Problem 71

Solve each equation and check the solution.
$$\frac{x}{3}+5=\frac{1}{6}$$

KB
Karan B.

Problem 72

Solve each equation and check the solution.
$$4 x-2=\frac{1}{2} x$$

Weston B.

Problem 73

Solve each equation and check the solution.
$$\frac{r}{5}+5=r-3$$

AG
Ankit G.
$$2(m-3)=-4$$