[ :~~ ~ ~?:~:::~ ~~~:~.i~~.: Choose the correct answer.. What is the solution of this system of equations? y=- = 7-4y A. (5,3) B. (3,-5) C. (-3,-5) D. (-5,3). Solve the system of equations. y=+5 y- = 3 A. (-3,-8) B. (-3,8) C. (3,-8) D. (3,8). 3. What is the solution of this system. of equations? 8 + 3y = -9 ~ -8 + Y = 9 o g. A. (3, -5) at>. ~ B. (3,5) "C ~ C. (-3, -5) 4. Solve the system of equations. 3 = Y + 4 -y=6 A. (-7, -) B. (-, -7) C. (, 7) D. (7, ) 5. Which system of equations has the solution (- 3, -0)? A. +y=7 + Y = 9 B. - Y = 7 3 - Y = -9 C. -y=7 3 + Y = -9 D. + y=-7 3 - Y = 9 ọ..., ~ D. (-3,5) CT o A Ui "C (3 :::y 5' ~ i! 79
',, I 6. Which system of equations does not have a solution? A. B. 6-7y = 5-4y = 0 6-7y = 5 A - 4y = - 0 \ \ c. 6 + 7Y = \~ \\ ls - y ~\" " D. 6 + 7y = 5 + 4y = 0 7. Which system of equations has infinitely many solutions? A. 6-3y = 9 4+ y= 6 A\ B. 6-3y = 6" \\ \ 4 - y = 9f\~'""- C. 6-3y = 9 \ 4 - y = 6 D. 6 + 3y = 9 4 + y = 3 8. Greta made the table below for the system of equations y = 3 + and y = - - 3. What can Greta conclude from the table?! - 3 + I'-I,' -,;",.,,:'t~'3~ X 'Y - ~ct -". - _3_~ ~~i_ S-..'.--~~ '-~~ - I -5 - t=tt---- - I - - - 3 ---,-- 4r-4--- [±~--- I 7-5 I 3 -i -0 i -6 A. The solution of the system of equations is (-, -). B. The solution of the system of equations is (-, - ). C. The system of equations has infinitely many solutions. D. There is no solution to the system of equations. _S:! C. ::> c 80 Chapter 5: Systems of Linear Equations
'r"'c'~~'~'h~'d"'e~~~pl~''''::-: ------------------." :..:,. ~. lesson 5: Systems oj Linear,Equations in Problem-Solving Situations Manuel has $54 to buy CDs and books. Each CD costs $9, and each book costs $6. He wants to buy eactly 7 items and to spend all his money. Write a system of equations that could be solved to determine Identify the variables. the number of CDs and the number of books Manuel buys. The variables are and _ Let c represent the number of CDs. Let b represent the number of books, Manuel wants to buy 7 items, so 7 = + ' A CD costs $, The total amount Manuel pays for CDs is multiplied by. The total cost for CDs is _ A book costs $, The total amount Manuel pays for books is _'_ multiplied by ' The total cost for books is _ Manuel has $54 to spend, Since he wants to spend all his money, this equals the sum of the cost of the CDs and books. That is, 54 = + ' A system of equations that can be solved to determine the number of CDs and the number of books Manuel buys is _ 83
r "L~~ ~~~ ~ p~~~t i ~~ l :.: Choose the correct answer.. The perimeter of a rectangular deck is 75 feet. The length of the deck, l, is 6 feet longer than times the width, w. Which system of equations can be solved to determine the length and width, in feet, of the deck? (Hint: The formula for the perimeter of a rectangle is P = + w.) A. + w = 75 = - 6w B. + w = 75 = w - 6 C. + w = 75 = 6 - w D. + w = 75 = 6 + w. The Mendez family is going to see a play. Adult tickets cost $9 and children's tickets cost $6. There are 6 people in the family, and they spend a total of $48 on tickets. Which system of equations can be solved to determine a, the number of adult tickets, and c, the number of children's tickets? A. 9a + 6c= 48 a+c=6 B. 9a + 6c= 48 a-c=6 C. 6a + 9c= 48 a+c=6 D. 6a + 9c= 48 a-c=6 3. A bo contains coins, consisting of quarters and dimes. The total value of the coins is $3.55. Which system of equations can be solved to determine the number of quarters, q, and number of dimes, d:in the bo? A. d + q = lad + 5q = 3.55 B. d + q = o.ioz + 0.5q = 3.55 C. d + q = 3.55 lad + 5q = D. d+ q = 0.0d + 0.5q = 355 4. When shopping for school supplies for her children, Mrs. Michaels bought sets of markers and 3 binders for a total cost of $. Mrs. Laurence bought 5 of the same sets of markers and of the same binders for a total cost of $5. How much binder A. $ B. $3 C. $4 D. $5 cost? does one j.s! C. :: c 84 Chapter 5: Systems of Linear Equations
.j..,. I 5. At the bulk foods store, cashews cost $5.00 per pound and pecans cost $7.00 per pound. ulian bought a 3-pound miture of cashews and pecans for $9.00. How many pounds each of cashews and pecans were in the mi? A. pounds of cashews and pound of pecans B..5 pounds of cashews and.5 pounds of pecans C. pound of cashews and pounds of pecans D. 0.5 pound of cashews and.5 pounds of pecans 6. Clarence bought 5 rolls of color film and 4 rolls of black-and-white film for his camera for a total of $4.00. The blackand-white film costs $.50 per roll more than the color film. How much does one roll of the black-and-white film cost? A. $.00 B.$.50 C. $3.50 D. $4.00 7. The perimeter of a rectangular garden is 00 feet. The length of the garden is 5 feet longer than times the width. What is the area of the garden? A. 450 square feet B. 55 square feet C. 600 square feet D. 65 square feet 8. A history test has 30 questions worth a total of 50 points. Every question is either multiple-choice or true-false. The true-false questions are worth 5 points each. The multiple-choice questions are worth 0 points each. Which system of equations can be used to determine how many multiple-choice questions, m, and how many true-false questions, t, are on the test? A. 0m + 5t = 50 m + t = 30 B. 5m + lot = 50 m + t = 30 C. 0m + 5t= 30 m + t = 50 D. 5m + lot = 30 m + t = 50 85
Chapter 5 Review..-. Use the graph for questions and., y "\ / 5- "\ 4 / / ~ "\ / - <, / / r-, -i -5-4 -3 - - 0V 3"-456 ~ '\ / I "\ 3 / -4 "'" / 5 / -i II Which is the solution ofthe system of equations? F (,) G (,) H (,) No solution 3 What is the value ofy in the solution of this system of equations?,which system of equations is represented by the graph? A y=+3 y = - + B y = - + 3 C y=-l y=-3 y=- D y = -3 y =- A 0 B C - D -0 3 - y = 4 y = 5.c. ::l o 86
Lessons 3-5 4 Tramain made the table below for the system of equations y = + and y = -3 +. y=+ y = -3 + -3-5 0 - -3 7 - o 3 Whatca~m the table?\ F G - 4 3 8 5 5 The solution of the system of equations is (5, 5). The solution of the system of equations is (, 5). H The system of equations has infinitely many solutions. There is no solution to the system of equations. 5 Amelia and Barrett sold a total of 37 raffle tickets at the football game. Barrett sold 0 fewer than twice as many as Amelia. How many tickets did Barrett sell? A 49 B 73 C 88 D 7 6 What is the solution of this system of equations? F (-, -9) G (-,9) H (3,) Not here 4-y= + y = 6 7 What is the value of in the solution of this system of equations? 5 - y = 8 3-4y = A B C D 3 5 "4 I 87
8 Which of these graphs could be used to find the solution for the following system of equations? F G y = - + 4 y=-5 y I I" I I'\.I 5 " 3 r-, '\. \3,h- -6-5 -4-3 - - 0 3" 4'\.5 6 - i r-, - -3-4 -7 II" y I,,( v v ~ V ~-3, ~~~rt- -6-0/' -3-0 3 4 5 6 - V I)' - -3-5 -6 y v '" 9 The graph below represents the following system of equations. I~ y = - - 4-7y = 3 y 5 " r-, 4 -, 3 r-, "-', -6-5-4-3-- N;, 3 4 6 - "-... )(.~ -5-4 -3 - - 0-3 4"'-5 6 "'- - -3-4 I' t -4 I"-.... -,... 5-6 Which of the followingis the best estimate ofthe solution for this system of equations? A (-~, -) B (0,-3~) C (~,-~) D (,-3~) " " H ~+4~r+r++--l~~,/~~'~ / -6-5 -4-3 - - 0 3/4 5 6 X I'\. : ~-t--i--t-+-l=~i~-+li'/<-t-+-t-h ~-t----t-+-l-3 A It,,-3-Hy I '''' A" 3~ ~,3)- - I"" "- I I -5-6.:: C. :l o 88 Chapter 5: Systems of Linear Equations
Lessons 3-5 0 Which system of equations has infinitely many solutions? F G H If the system of equations given below has no solution, what is the value of k? Mariano has $3.55 in nickels and quarters. The total number of coins is 5 less than twice the number ofnickels. Which system of equations can be used to determine q, the number of quarters, and n, the number of nickels, that Mariano has? F n + q = 3.55 n + q - 5 = n G n + q = 3.55 n + q = 5 - n H O.05n + O.5q = 3.55 n + q = 5 - n O.05n + O.5q = 3.55 n + q = n - 5 + 4y = 8 3+ky=8,, Record your answer and fill in _t~ ' bubbles below.be sure to use ~E\ correct place value. G 0 0 0 G 0 CD CD CD CD CD CD CD CD CD CD CD o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c ~ n' ~ 5' ao. O :> -c -0 O ;::+ 0... ::r 0;' 0-0 0 "0;' -0 a::r 0' ~ "- m?' 89
3 Mr. Harris bought 4 hot dogs and 3 veggie burgers for his family from a refreshment stand at the beach and paid $7. Ms. Saunders bought 7 hot dogs and 4 veggie burgers for her family at the same refreshment stand and paid $4. A. Write a system of equations that can be used to determine h, the price of a hot dog, and v, the price of a veggie burger. B. Solve your system of equations algebraically. Show your work. C. Interpret your solution in terms of the situation. 90 Chapter 5: Systems of Linear Equations