Systems of Linear Equations

1 The sum of Ken's, k, and Alan's, a, ages is 62. Ken is 31 years older than Alan. 3 The following system of equations is shown below. Which of these systems of equations below best describes the ages of Ken and Alan? A k + a = 61 k = 31 B k + a = 62 a k = 31 C k + a = 62 k a = 31 D k + a = 62 a = k + 31 2 Janie needs to solve the system of linear equations below for her homework assignment. y = 14 x 20 y = x 7 Which of the following is a reasonable estimate of the solution to this system of linear equations? F G H J 2x + 3y = 4 x y = 3 Which of the below is the solution to this system? A ( 13,10) B ( 1,2) C (1, 2) D (2,3) 4 Charlie is making a rectangular picture frame. The height of the frame is 6 inches longer than its width. The perimeter of the frame is 76 inches. Which of these systems of equations below best describes the dimensions of the picture frame? F h + w = 6 h + w = 76 G h w = 6 2h + 2w = 76 H h + w = 6 2h + 2w = 76 J h w = 6 h w = 6 Page 3

5 A system of equations is shown below. 3x + 2y = 12 y = x + 1 Which ordered pair below represents the solution to this system of equations? A (1.25,2.25) B (2,3) C (2.2,3.2) D (3,2) 6 The following system of equations is shown below. 4x 2y = 7 3x + 3y = 10 Which of these points below represents the intersection of the equations? F G H J Page 4

7 The tables below represent values that correspond to a system of equations. Equation A Equation B What is the solution to this system of equations? A ( 2,6) B (0,2) C ( 1, 5) D (1,0) Page 5

8 Ted's Taxi Service has cabs that can seat 4 people each and vans that can seat 15 people each. The taxi service can transport a maximum of 134 people in its 17 units. 9 A total of 1,650 tickets were recently sold at Friday night's football game. Each adult ticket cost $3.50, and each student ticket cost $2.00. The total revenue for ticket sales was $4,650. The system of linear equations below models this situation. x + y = 17 4x + 15y = 134 If x represents the number of cabs at Ted's Taxi Service, and y represents the number of vans at Ted's Taxi Service, which is a reasonable estimate of the solution to this system of linear equations? F Ted owns only one van. Determine a, the number of adult tickets sold, and s, the number of student tickets sold. A 3.50a + 2.00s = 4,650 a + s = 1, 650 B 350a + 200s = 4,650 a + s = 1,650 C 3.50a + 2.00s = 1,650 a + s = 4,650 D 350a + 200s = 1,650 a + s = 4,650 G H J Ted owns more vans that cabs. Ted owns more cabs than vans. Ted owns the same number of vans as cabs. Page 6

10 Brenda needs to solve the system of linear equations below for her homework assignment. y = 9x 70 y = 2x 32 Which is a reasonable estimate of the solution to this system of linear equations? F (8, 25) G (7, 24) H (5, 22) J (3, 20) Page 7

11 Al's Movies charges $7.00 for a membership and $1.00 per each movie rental. Beth's Videos has no membership fee and charges $2.75 per movie rental. The table below shows the movie charges for each store. Number of movies Cost at Al s Movies Cost at Beth s Videos 0 $7.00 $0.00 1 $8.00 $2.75 2 $9.00 $5.50 3 4 5 6 What is the number of videos a customer would need to rent from each store for the cost to be the same? A 3 B 4 C 5 D 6 Page 8

12 Cathy wants to use the substitution method to solve this system of equations. 13 Juan correctly found a table of values for each equation in a system of equations, as shown below. The four steps below show how she solved the following system of equations. x + y = 5 2x + 3y = 10 Step 1: y = 5 x Step 2: 2x 15 x = 10 Step 3: x 15 = 10; x = 25 Step 4: y = 5 25; y = 20 In which step did the first error occur? F Step 1 G Step 2 H Step 3 J Step 4 Solutions of 1st equation x y 0 9 1 7 2 5 3 3 Solutions of 2nd equation x y 0 4 2 5 4 6 6 7 What is the value of x in the solution to this system of equations? A 0 B 2 C 3 D 5 Page 9

14 The table below shoes the rates for two duplicating companies. Quick Copy Copy Place Initial Fee of Initial fee of $5.00 $10.00 $0.06 per page$0.04 per page The total cost, c, is dependent on the number of pages, p, that are duplicated. Which of these systems of equations represents this situation? F p = 5 + 6c p = 10 + 4c G c = 5 + 6p c = 10 + 4p H p = 5 + 0.06c p = 10 + 0.04c 15 A college football team scored 12 times in a game, for a total of 72 points. Each touchdown is worth seven points and each field goal is worth three points. Which system of equations below could be used to solve for x, the number of points the team scored from touchdowns, and y, the number of points the team scored from field goals? A x + y = 12 7x + 3y = 72 B x + y = 72 7x + 3y = 12 C D J c = 5 + 0.06p c = 10 + 0.04p Page 10

16 Angola High School sold three times as many children's tickets as adult tickets for the school play. The total amount collected was $357.50. Children's tickets cost $1.50 each, and adult tickets cost $2.00 each. Which system of equations below could be used to determine c, the number of children's tickets, and a, the number of adult tickets, that were sold? F 1.50a+2c= 357.50 3a+c = 357.50 G 1.50a+2c = 357.50 3c=a H 1.50c+2a = 357.50 3c = a J 1.50c+2a = 357.50 3a = c 17 Joey collects football cards and baseball cards. He has a total of 160 cards. The number of football cards, f, is 12 more than twice the number of baseball cards, b. Which system of equations below could be used to find out how many football cards and baseball cards Joey has? A f + b = 160 f = 2b + 12 B f = 2b f 12 = 2b C f b = 160 f + b = 2b D f + b = 160 f = 2b 12 Page 11

18 Naomi took a 40 question history exam. The exam had only multiplechoice questions and short answer questions. Each multiple choice question was worth one point; each short answer question was worth five points; the whole exam was worth 100 points. Which system of equations below could be used to solve for m, the number of multiple choice questions, and s, the number of short answer questions? F s + m = 40 5s + m = 100 G 5s + m = 40 s + m = 100 H m + s = 40 5m + s = 100 J 5m + s = 40 m + s = 100 Page 12

19 What is the value of x in the solution to the system of equations below? 6x + 3y = 13 3x y = 4 A 1 B C D Page 13 BE SURE YOU HAVE RECORDED ALL OF YOUR ANSWERS ON YOUR ANSWER DOCUMENT STOP