When using the addition or substitution method, how can you tell if a system of linear

In Exercises 1-4, determine whether the gh1tm ordered pair is a solution of the system. (2, 3) { .\' + 3\ - 11 X - 5y - - 13

In Exercises 1-4, determine whether the gh1tm ordered pair is a solution of the system. (- 3, 5) { 9x + 7y - 8 &r - 9y - - 69

In Exercises 1-4, determine whether the gh1tm ordered pair is a solution of the system. (2,5) { 2r + 3y - 17 X+ 4y - 16

In Exercises 1-4, determine whether the gh1tm ordered pair is a solution of the system. (8,5) { 5x - 4y - 20 3y - 2 t + 1

In Exercises 5-18, solve each system by the substituHon method. { ' + y - 4 y - 3x

In Exercises 5-18, solve each system by the substituHon method. { ' + y - 6 y - 2x

In Exercises 5-18, solve each system by the substituHon method. {' + 3y - 8 y - 2t - 9

In Exercises 5-18, solve each system by the substituHon method. {2r - 3y - - 13 y - 2t + 7

In Exercises 5-18, solve each system by the substituHon method. {' - 4y - 2 x - 6y + 8

In Exercises 5-18, solve each system by the substituHon method. {' - 3y + 7 X - 2y - 1

In Exercises 5-18, solve each system by the substituHon method. ex + 2y - O X - 3y - 0

In Exercises 5-18, solve each system by the substituHon method. 4x + 3y - 0 2r - y - 0

In Exercises 5-18, solve each system by the substituHon method. ex + 5y - - 4 lr - y - 11

In Exercises 5-18, solve each system by the substituHon method. {2r + 5y - 1 - x + 6y - 8

In Exercises 5-18, solve each system by the substituHon method. {2r - 3v - 8 - 2t 3x + 4y - x + 3y + 14

In Exercises 5-18, solve each system by the substituHon method. ex -4y - X - )' + 4 2r+ 6y - 5y - 4

In Exercises 5-18, solve each system by the substituHon method. ('-H H ( 'r'- 2

In Exercises 5-18, solve each system by the substituHon method. ('-+3 " .v - 'r'- 2 y - rx

In Exercises 19-30, solve each system by the addition method. {X + )' - ~ 20. {X + )' - 6 X - J - .:>

In Exercises 19-30, solve each system by the addition method. X + )' - 6 X - J - .:> X - J - - 2

In Exercises 19-30, solve each system by the addition method. 2r + 3y - 6 2r - 3y - 6

In Exercises 19-30, solve each system by the addition method. {1r + 2v - 14 3x - 2y - 10

In Exercises 19-30, solve each system by the addition method. { x + 2y - 2 {2t - 7v - 2 ' -4x + 3y - 25

In Exercises 19-30, solve each system by the addition method. 2t - 7v - 2 ' -4x + 3y - 25 24 3x + y - - 20

In Exercises 19-30, solve each system by the addition method. {4x + 15 2r - ))' - 1

In Exercises 19-30, solve each system by the addition method. 1t - 7y - 13 lit + 5y - 7

In Exercises 19-30, solve each system by the addition method. {1t - 41' - 11 2r + 3y - - 4

In Exercises 19-30, solve each system by the addition method. 2r + 3y - - 16 5x - lOy - 30

In Exercises 19-30, solve each system by the addition method. {1t - 4y +1 3y - ] - 4.t

In Exercises 19-30, solve each system by the addition method. ex - 6y +40 2y - 8 - 3x

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. {X - 9 - 2y x + 2y - 13

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. t'it + 2y - 7 y - 2 - 3x

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. \ - 3x - 5 21x - 35 - 7y

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. {9.t - 3y - 12 y - 3x - 4

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. {1r - 2y - - 5 4x + y - 8

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. {2r + 5y - - 4 3x - y - 11

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. { X + 3y - 2 1t + 9y - 6

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. 4x - 2y - 2 2t - y - 1

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. X + 4y - - 9

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. 6 - 2 - 3 X + 4y - - 9 .t + 2y --3

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. {2r - 3y + 4 4 ' - X - .> - )J

In Exercises 31-42, solve by the method of your choice. Jdemify systems with no solution and systems with infinitely many solufUms. using set notation to express their solution sets. ex - - 3y + 8 2r - - t4 + 'Y

In Exercises 43-46. let x represellt one number and let y represenT the other numbe1: Use the given conditions ID write a system of equations. Solve the system and find the numbers. 11te sum of two numbers is 7. 1f one number is subtracted from the other, Lheir difference is - 1. Find the numbers.

In Exercises 43-46. let x represellt one number and let y represenT the other numbe1: Use the given conditions ID write a system of equations. Solve the system and find the numbers. l l1e sum of two numbers is 2. If one numbe r is subtracted from the other. their differe-nce i.s 8. Ftnd the numbers.

In Exercises 43-46. let x represellt one number and let y represenT the other numbe1: Use the given conditions ID write a system of equations. Solve the system and find the numbers. 11uee times a first number dec.reased by a second number is 1. The first number increased by twice the second number is 12. Find the numbers.

In Exercises 43-46. let x represellt one number and let y represenT the other numbe1: Use the given conditions ID write a system of equations. Solve the system and find the numbers. 11te sum of three times a first number and twice a second number isS. If the second number is subtracted from twice the first number. the result is 3. Find the numbers.

In Exercises 47-48. solve each system by the flU!-Ihod of your choice. x+2 y+4 ------3 7 2 3 x+y ,?. 5 2 2

In Exercises 47-48. solve each system by the flU!-Ihod of your choice. x;y _x;y -I x..t.2 y +4 --2 3 -4---

In Exercises 49--50, solve e.ach system for x andy, expressing either l'a/ue in terms of a or b. if mxessmy. Assrtme thm a # 0 and b F 0. 5ax + 4y - 17 ax + 7y - 22

In Exercises 49--50, solve e.ach system for x andy, expressing either l'a/ue in terms of a or b. if mxessmy. Assrtme thm a # 0 and b F 0. 4ax + by - 3 6ax + )by - 8

For the linear runction f(x) - 111x + b,f(- 2) - 11 and !(3) - - 9. Find 111 and b.

For the linear runction f(x) - 111x + b,j(- 3) - 23 and !(2) - - 7. Find 111 and b.

Use the graphs of the linear functions to solve Exercises 53-54. Write the linear system whose solution set is j(6, 2)1. Express each equation in the system in slope -intercept fom1.

Use the graphs of the linear functions to solve Exercises 53-54. Write the linear system whose solution set is 0. Express each equation in the system in slope -intercept foml.

The figure shows the graphs of the cost and revemre fimclions for a company that manufacwres and sells small radios. Use the information in the figure to solve Exercises 55-60. y 35,000 30.000 25,000 20.000 15,000 10.000 5000 C[rf - 10,000 + 30.r ;"-~;--,;:i:;;-~;;-~-;:!:;;-~-:;;~.r 100 200 300 400 500 600 700 Radios Produced and Sold How many radios must be produced and sold for lhe company to break even?

The figure shows the graphs of the cost and revemre fimclions for a company that manufacwres and sells small radios. Use the information in the figure to solve Exercises 55-60. y 35,000 30.000 25,000 20.000 15,000 10.000 5000 C[rf - 10,000 + 30.r ;"-~;--,;:i:;;-~;;-~-;:!:;;-~-:;;~.r 100 200 300 400 500 600 700 Radios Produced and Sold More than how many radios must be produced and sold for the company to have a profit?

The figure shows the graphs of the cost and revemre fimclions for a company that manufacwres and sells small radios. Use the information in the figure to solve Exercises 55-60. y 35,000 30.000 25,000 20.000 15,000 10.000 5000 C[rf - 10,000 + 30.r ;"-~;--,;:i:;;-~;;-~-;:!:;;-~-:;;~.r 100 200 300 400 500 600 700 Radios Produced and Sold Use the formulas shown in the voice balloons to find R(200) - C(200). Describe what lhismeans rorthecompany.

The figure shows the graphs of the cost and revemre fimclions for a company that manufacwres and sells small radios. Use the information in the figure to solve Exercises 55-60. y 35,000 30.000 25,000 20.000 15,000 10.000 5000 C[rf - 10,000 + 30.r ;"-~;--,;:i:;;-~;;-~-;:!:;;-~-:;;~.r 100 200 300 400 500 600 700 Radios Produced and Sold Use the formulas shown in the voice balloons to find R(300) - C(300). Describe what lhismeans rorthecompany.

The figure shows the graphs of the cost and revemre fimclions for a company that manufacwres and sells small radios. Use the information in the figure to solve Exercises 55-60. y 35,000 30.000 25,000 20.000 15,000 10.000 5000 C[rf - 10,000 + 30.r ;"-~;--,;:i:;;-~;;-~-;:!:;;-~-:;;~.r 100 200 300 400 500 600 700 Radios Produced and Sold a. Use the formulas shown in the voice balloons to write the company's profit function, P, fTom producing and selling x radios.. b. Fond the company's profit if 10.000 radios are produced and sold.

The figure shows the graphs of the cost and revemre fimclions for a company that manufacwres and sells small radios. Use the information in the figure to solve Exercises 55-60. y 35,000 30.000 25,000 20.000 15,000 10.000 5000 C[rf - 10,000 + 30.r ;"-~;--,;:i:;;-~;;-~-;:!:;;-~-:;;~.r 100 200 300 400 500 600 700 Radios Produced and Sold a. Use the formulas shown in the voice balloons to write the company's profit function, P, fTom producing and selling x radios. b. Fond the company's profit ir 20,000 radios a re produced and sold.

Exercises 61-64 describe a number of business ventures. For each exercise, a. Write the cost function, C. b. Write the revenue function, R. c. Determine the break--even point. Describe whal this means. A company that manuractures small canoes has a fixed cost of $18,000. ll costs $20 to produce each canoe. me selling price is $80 pe r canoe. (In solving this exercise. let x represent the number of canoes produced and sold.)

Exercises 61-64 describe a number of business ventures. For each exercise, a. Write the cost function, C. b. Write the revenue function, R. c. Determine the break--even point. Describe whal this means. A company that manufactures bicycles has a fixe.d cost or $100.000. It costs $100 to produce each bicycle. 'llle selling price is $300 per bike. (In solving this exercise, le t .\' represent the number of bicycles produced and sold.)

Exercises 61-64 describe a number of business ventures. For each exercise, a. Write the cost function, C. b. Write the revenue function, R. c. Determine the break--even point. Describe whal this means. You invest in a new play. The cost includes an overhead or $30,000, plus production costs of $2500 per pe rfom1ance. A sold-out pe rfom1ance brings in $3125. (In solving this exercise., le t x represent the number of sold-out performances.)

Exercises 61-64 describe a number of business ventures. For each exercise, a. Write the cost function, C. b. Write the revenue function, R. c. Determine the break--even point. Describe whal this means. You invesled $30,000 and started a business writing greeting ca rds. Supplies cost 2 per card and you are selling each card for 50. (In solving this exercise, let x represent the number of cards produoed a nd sold.)

An important appliroJiotl of syslerns of equations mi'ies in connlion with supply and demand. As the price of a product increases. the demand for that producJ de.aeases. Howt!l'e.t; at higher prices, suppliers are willing to produce gremer quamities of the product. 111e price at which supply and demand are equal is called the equillbriwn price. 111e quantity supplied and demanded at that price is called the equilibrium quantity. Exercises 65-66 involve supply aJUJ demand. ll1e following models describe wages for low-skilled labor. p - - 0.325x + 5.8 Pri.co of labor (per houri Millioflt tf WtUn .. , loyert will .i,.. Supply Model p - 0.315x + 3 Pric.t of lshr (ptt hoe.rt Millio11t tf n'tila&lo .-orkett Source: O'Sullivan and Sheffrin, Emnomics, Prentice Hall, 2007. a. So lve the system a nd find the equilibrium number of workers, in millions, and the equilibrium hourly wage. b. Use your answer from pa rt (a) to complete this statement: 1r workers are paid ___ pe r hour, there will be __ million available workers and __ million workers will be hired. c. In 2007, the federal minimum wage was set at S5.15 per hour. Substitute 5.15 for p in the demand model, p - - 0.325x + 5.8, and determine the millions of workers employers will hire at this price. d. At a minimum wage of $5.15 pe r hour, tL'\C the supply model, p - 0315x + 3, to determine the millions of available workers. Round to one decimal place. e. Al a minimum wage of$5.15 per hour, use your answers from parts (c) and (d) to detem1ine how many more people are looking for work than employers are willing to hire.

An important appliroJiotl of syslerns of equations mi'ies in connlion with supply and demand. As the price of a product increases. the demand for that producJ de.aeases. Howt!l'e.t; at higher prices, suppliers are willing to produce gremer quamities of the product. 111e price at which supply and demand are equal is called the equillbriwn price. 111e quantity supplied and demanded at that price is called the equilibrium quantity. Exercises 65-66 involve supply aJUJ demand. 111e following models describe demand and supply for threebedroom rental apartments.. Demand Model p - - 50x + 2000 Moet.ly rutal price; N~mbtr o oputmuts 4tmlll4d, in thouudt Supply Model p - 50x Monthly reahl triu Nber or putmub n pplid, i tho11tud.sa. Solve the system and find the equilibrium quantity and the equilibrium price. b. Use your answer from pa rt (a) to complete this statement: 'When rents are ___ per month, consumers will demand apartments and suppliers ''~II offer ___ apartments for rent.

The bar graph indic.ates that fewer U.S. adults are getting married. Marital Status of U.S. Adults ro% 70% 60% 50% 40% 30% 20% 10% 111e data can be modeled by the following system of linear equations: { - 3x + lOy - 160 X + 2y - 142. Puuatago tf U'fer-nurriod A11ericu eitlh, y, x pm efter 1970 Percutes of murie.l Americ.u dulft, y, x yem after 1970 a. Use these models to detem1ine the year, rounded to the nearest year, when the percentage of nevcr.married adults will be the same as the percentage of married adults. For that year ,approximately what percentage of Americans, rounded to the nearest percent, will belong to each group? b. How is your approximate solution from part (a)shown by the following graphs? )' ro 70 60 50 40 30 Nem x~ty-142 Married 20 L,.::;.::.:.:;::--- - 3x + lOy - 160 10 '--:l:---:::!:----.t:----.!!:----7.~+.--t.~;;!:--.r 10 20 30 40 50 60 70M 90 Years a~er 1970

The bar graph shows the percentage of Americans for and against the death penalty for a person convicted oF murder. 100% ro% 79 Are You in Faor of the Death Penalty for a Person Con,icted of Murder? ro For the death penalty Against the death penalty Source: Newsweek poll The data can be modeled by the followingsystem of equations: { 13x + 12)' - 992 - x + y - 16. fhe percent, y, in tam ef th 4nt pendty X yeeu e(tu 1983 fbe petcn:l, y, aseiut tDe 4t;tli peaalty x yeert aftn 19!4 In whic.h year will the percentage of Americans in favor of the death penalty be the same as the percentage of Americans who oppose it? For that year, what percent will be for the death penalty and what percent will be against it?

We opened this section with a study showing that late in the semester, procrastinating students reported more symptoms of physical illness than their nonprocrastinating peers. a. At the beginning of the semester, procrastinators reported an average of 0.8 symptoms, increasing a t a rate of 0.45 symptoms pe r week. Write a function that models the average number of symptoms after x weeks. b. At the beginning of the semester, nonprocrastinators reporled an average of 2.6 symptoms, increasing a t a rate of 0.15 symptoms per week. Write a function that models the average number o r symptoms after x weeks. c. By which week in the semester did both groups report the same number of symptoms of physical illness? For that week, how many symptoms were reported by each group? How is this shown in figure 5.1 on page 5t6t

Although Social Security is a problem, some projections indicate that there's a much bigger time bomb tic.king in the federal budget. and that's Medicare. in 2000, the cost of Social Security was 5.48% of the gross domestic product, inc.reasing by 0.04% of the GOP per year. In 2000. the cost of Medicare was 1.84% of the gross domestic product, increasing by 0.17% of the GOP per year. (Source: Congressional Budget Office) a. Write a function that models the cost of Social Security as a percentage of the GOP x years after 2000. b. 'Write a function that models the cost of Medicare as a percentage of the GOP x years after 2000. c. In which year will the cost of Medicare and Social Security be the same? For that year, what will be the cost of each program as a percentage of the GOP? Which program will have the greater cost a fte r that year?

The graphs show the percentage of American adults in two living arrangements from 1960 through 2008. 60% 50% 40% 30% 20% 10% Living Arrangements nf U.S. Adults 1t960, 471 I200S, 171 1t960, Sl u'ing ltOOS, t41 Alone ... 1960 1970 1980 t 990 2000 2008 Year Souroe: U.S. Census Bureau a. Write the slope-intercept equation of the line that models the percentage of U.S. adults living a lone, y, x years after 1960. Round the ''alue of the slope, m, to one decimal place. b. 'Write the slope-intercept equation of the line that models the pe rcentage o f married U.S. aduJlS living with kid-s. y. x years after 1960. Round the value of the slope, m, to one decimal place. r. Use the models fTOm parts (a) and (b) to project the year in which the percentage of adults living alone will be the same as the percentage of married adults living \\~th kids. What percentage of U.S. adults will belong to each group during that year?

The graphs show that the U.S. public has taken a more conservative sta nce on gun control for the period from 1999 through 2009. ~ 70% 60% 50% 40% 30% 20% 10% ~ U.S. Pub r Opinion on Gun Control fa,orGun lt999, 6S) Control 1t009, 491 _. 1t999, 301 A~ Gun lt009, 4SI .... ntrol 1999 2001 2003 2005 2007 2009 Year Source.: pewresearch.org a. Write the slope-intercept equation of the line that models the percentage of the U.S. public that favors gun control,)'. x years after 1999. b. \Vrite the slope-intercept equation of the line that models the percentage o f t he U.S. public against gun control, y} x years after 1999. r. Use the models from parts (a) and (b) to project the year, to the nearest whole year, d uring whic.h the percentage in favor of gun control was the same as the percentage against gun control. What percentage of the U.S. public, to the nearest percent, shared each of these opinions during that year?

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2005 One Mr. Goodbar and two Mounds bars contain 780 calories. Two Mr. Good bars and one Mounds ba r conta in 786 calories. Find the caloric conte nt of each candy bar.

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2006 One Snickers bar a nd two Reese's Peanut Butte r Cups conta in 737 caloric.~. Two Snickers bars and one Reese's Peanut Butter Cup contain 778 calories. Find the caloric contcnf each candy bar.

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2007 A cou.tion of Halioween candy contains a total of five Mr. Gdddbars and Mounds bars. Chew on this: llte grams of fat in these candy bars exceed the daily ma..ximum desirable fat intake of 70 grams by 7.1 grants. How many bars of each kind of candy are contained in the Ha lloween collection?

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2008 A collection of HaJioween candy contains a total of 12 Snickers bars and Reese's Peanut Butte r Cups. Chew on this: The grams of fat in these candy bars exceed twice the daily maximum desirable fat intakeof 70grams by 26.5 grams. How many bars of each kind of candy are contained in the Halloween collection?

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2009 A hotel has 200 rooms. Those with kitchen facilities rent for $100 pe r night a nd those without kitchen facilities re nt for $80 per night. On a night when the hotel was completely occ.upied, revenues were $17,000. How many of each type of room does the hotel have?

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2010 A new restaurant i.s to contain two-seat tables and four-seat tables. Rre codes limit the restaurant's maximum occupancy to 56 customers. If the owners have hired enough servers to handle 17 tables of customers, how many of each kind of table should they purchase?

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2011 A rectangular lot whose perimeter is 360 feet ls fenced along three sides. An expensive fencing a long the Jot's length costs $20 per foot and an inexpensive fencing along the two side widths costs only S8 per foot. The total cost of the fenc.ing along the three sides comes to $3280. What are the lot's dimensions?

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2012 A rectangular lot whose perimeter is 320 feet is fenced along three sides. An expensive fencing aJong the lot's length costs $16 per foot and an inexpensive fencing along the two side widths costs only SS per foot. The total cost of the fencing along the three sides comes to $2140. What are the lot's dimensions?

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2013 When a crew rows with the current, it travels 16 miles in 2 hours. Against the current, the crew rows 8 miles in 2 hours. Let x - the crew's rowing rate in still water and let y - the rate of the current. Tlle following chart summarize.<; this infom1ation: Rate X lime ~ Dis1ance Rowing with x+y 2 16 current Rowing against x - y 2 8 current Find the rate of rowing in still water and the rate of the current.

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2014 When an airplane flies \\~th the wind, it travels 800 miles in 4 hours. Against the wind, it takes 5 hours to cover the same distance. Find the plane's rate in still a ir a nd the rate of the wind.

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2015 In Exercises 83-84, 011 isosceles triangle co111ahJing two angles with equal measure is shown The degree measure of each triangle's three itHerior angles and an exterior atJgle is represetlted witiJ variables. Find the measure of the three iJJterior angles.

Use a system of linear equations to solve Exi!rdses 73-84. Looking for Mr. Goodbar? It's probably not a good idea if you want lo look like Mr. UtJiverse or Julia Roberts. The graph shows the four candy bars with the highest fat contem. representing grams of fat and calories in each bar. Exercises 73- 76 are based on the graph. 17 16 15 14 13 12 11 Candy Bars w~h the Highest Fat Content Fat (grams) Calories Source: Krantz and Sveum, 111e \Vorlds Worsts. arpe Colli n~ 2015 In Exercises 83-84, 011 isosceles triangle co111ahJing two angles with equal measure is shown The degree measure of each triangle's three itHerior angles and an exterior atJgle is represetlted witiJ variables. Find the measure of the three iJJterior angles.

What is a system of linear equations? Provide an example with your description.

What is the solution of a system of linear equations?

Explain how to solve a system o f equations using the substitution method. Use y - 3 - 3x and 3x + 4y - 6 to illustrate your explanation.

Explain how to solve a system of equations using the addition method. Use 3x + 5y - - 2 and 2x + 3y - 0 to illustrate your explanation.

When is it easier to use the addition method rather than the substitution method to solve a system of equations?

When using the addition or substitution method, how can you tell if a system of linear equations has infinitely many solutions? What is the relationship be tween the graphs of the two equations?

When using the addition or substitution method, how can you tell if a system of linear equations has no solution? What is the relationship between the graphs of the two equations?

Describe the break-even point for a business.

Verify your solutions to any five exercises in Exercises 5-42 by using a graphing utility to graph the two equations in the system in the same viewing rectangle. Then use the intersection feature to display the solution.

In Exercises 94-97. determine whdhereach statemcml makes Sl!JISe or does no/. make SC'JJSI!, and explain your reasoning. Even if a linear system has a solution set involving fractions. suc-h as {(it,#)}, I can use graphs to detem1ine if the solution set is reasonable.

In Exercises 94-97, determine whdhereach statemcml makes Sl!JISe or does no/. make SC'JJSI!, and explain your reasoning. Each equation in a syste.m of linear equations has infinitely many ordered-pair solutions.

In Exercises 94-97. determine whdhereach statemcml makes Sl!JISe or does no/. make SC'JJSI!, and explain your reasoning. Every linear system has infinitely many ordered-pair solutions.

In Exercises 94-97. determine whdhereach statemcml makes Sl!JISe or does no/. make SC'JJSI!, and explain your reasoning. If I know the pe rimeter of this rectangle a nd triangle, each in the same unit of measure, I can use a system of linear equations to determine values for x andy. y y

Write a system of equations having ((- 2. 7)1 as a solution set. (More than one system is possible.)

Solve the system for x a nd y in terms of a1.bt. c1 ,a1,b2, and c2: { a 1x + b1y - c1 ~ + bl)' - c2

Two identical twins can only be distinguished by the characteristic that one always te-lls the truth and the other always lies. One twin tells you of a lucky number pair: '"'\Vhen I multiply my first lucky numbe r by 3 and my second lucky numbe r by 6, the addition of the resulting numbe rs produces a sum of 12. When I add my first lucky number a nd twice my second lucky number, the sum is 5."Which t\\~n is talking?

A marching band has 52 members, and there are 24 in the pom-pom squad. They wish to form several hexagons a nd squares like those diagrammed below. Can it be done with no people left over? 8 8 p p 8 - Band Member B P 8 B P - Pom-pom Person 8 B p p

The group should write four different word problems that can be solved using a system of linear equations in two variables. All of the problems should be on different topics. The group should turn in the four problems and their algebraic solutions.

Exercises 103-105 will help you prepare for lire material covered nlhe next section. Jr x - 3.y - 2. and z - - 3, does the ordered triple (x,y, z)satisfytheequation 2x - y + 4z - - 87

Exercises 103-105 will help you prepare for lire material covered nlhe next section. Consider the following equations: { 5x - 2y - 4: - 3 Equation 1 3x + 3y + ~ - - 3. Equation 2 Use this process to eliminate z: Copy Equation 1 and multiply Equation 2 by 2.Then add the ua tion~

Exercises 103-105 will help you prepare for lire material covered nlhe next section. Write an equation involving a, b. and c based o n the oll \\~ng description: When the value o r X in y - ail + bx + c is 4, lhe value or }' is 1682.