Warm-Up Solve the following systems of equations using the method of your choice x – 9y = y = -3x x + y = 20 4x + 9y = 23 5x – 4y = -3 6x – 5y = 12

1. -2x – 9y = -25 4x + 9y = 23 2x = -2 x = -1 Elimination 4x + 9y = 23 4(-1) + 9y = y = 23 9y = 27 y = 3 (-1, 3)

2. y = -3x + 5 5x - 4y = -3 5x – 4(-3x + 5) = -3 5x + 12x – 20 = -3 17x – 20 = -3 17x = 17 x = 1 Substitution y = -3x + 5 y = -3(1) + 5 y = 2 (1, 2)

3. 2x + y = 20 6x – 5y = 12 -6x – 3y = y = -48 y = 6 Elimination ( ) x -3 2x + y = 20 2x + (6) = 20 2x = 14 x = 7 (7, 6)

When could you use System of Equations?

Define your variables. Set up your equations. Solve. 1. You have a money jar containing nickels and quarters worth $1.55. The money jar contains 11 coins. How many of each coin do you have? n = # of nickels q = # of quarters.05n +.25q = 1.55 n + q = 11 Elimination.05n +.25q = 1.55 n + q = n -.05q = q = 1 q = 5 ( ) x nickels and 5 quarters n + q = 11 n + (5) = 11 n = 6

Define your variables. Set up your equations. Solve. 2. Your teacher gives you a test worth 100 points with 40 questions. Each question is worth either 2 points or 4 points. How many 2 point questions are on the test? How many 4 point questions are on the test? t = # 2 point questions f = # of 4 point questions 2t + 4f = 100 t + f = 40 Elimination 2t + 4f = 100 t + f = 40 -2t – 2f = -80 2f = 20 f = two pointers and 10 four pointers ( ) x -2 t + f = 40 t + (10) = 40 t = 30

Define your variables. Set up your equations. Solve. 3. You are buying supplies for a party. You buy three rolls of streamers and 15 party hats and spend $30. Later you bought two rolls of streamers and four party hats and spent $11. How much did each roll of streamers cost? How much did each party hat cost? r = price per streamers h = price per hat 3r + 15h = 30 2r + 4h = 11 Substitution 3r + 15h = 30 3r = h r = 10 – 5h 2r + 4h = 11 2(10 – 5h) + 4h = – 10h + 4h = – 6h = 11 -6h = -9 h = 1.5 2r + 4h = 11 2r + 4(1.5) = 11 2r + 6 = 11 2r = 5 r = 2.5 $1.50 per streamer and $2.50 per hat

Define your variables. Set up your equations. Solve. 4. Darcie and Mattie are picking up trash along the highway. Together they have collected 16 bags of trash. Darcie has collected 4 bags more than Mattie. How many bags did Darcie collect? How many bags did Mattie collect? d = # bags collected by Darcie m = # bags collected by Mattie d + m = 16 d = m + 4 Substitution d = m + 4 d + m = 16 (m + 4) + m = 16 2m + 4 = 16 2m = 12 m = 6 d = m + 4 d = (6) + 4 d = 10 Darcie collected 10 bags and Mattie collected 6

5.The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank charges an annual fee of $17 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost? a) 3 games; $22 b) 2 games; $16 c) 4 games; $27 d) 6 games; $38

6. At a farmers' market cucumbers cost $1.10 per pound and carrots cost $1.40 per pound. Mrs. Lamb bought two pounds more cucumbers than carrots and spent $9.70. How many pounds of each did she buy? a) 4 pounds of cucumbers and 2 pounds of carrots b) 2 pounds of cucumbers and 4 pounds of carrots c) 5 pounds of cucumbers and 3 pounds of carrots d) 3 pounds of cucumbers and 5 pounds of carrots

7. Julia and Missy went shopping and spent $320 altogether. Julia spent $100 more than Missy spent. How much did Missy spend? a) $100 b) $110 c) $210 d) $200

8. Tickets to a museum cost $5.00 for general admission and $2.00 with a student ID. On Friday night 200 tickets were sold for a total of $625. How many general admission tickets were sold? a) 125 b) 135 c) 85 d) 75

HOMEWORK

You sell tickets for admission to your school play and collect a total of $104. Admission prices are $6 for adults and $4 for children. You sold 21 tickets. How many adult tickets and how many children tickets did you sell? 6a + 4c = 104 a + c = 21

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80 and some order the steak dinner for $17. If the total bill was $91, how many people ordered each type of dinner? c + s = c + 17s = 91

You bought the meat for Saturday’s cookout. A package of hot dogs cost $1.60 and a package of hamburger cost $5. You bought a total of 8 packages of meat and you spent $23. How many packages of hamburger meat did you buy? d + h = d + 5h = 23

Casey orders 3 pizzas and 2 orders of breadsticks for a total of $ Rachel orders 2 pizzas and 3 orders of breadsticks for a total of $23. How much does a pizza cost? 3p + 2b = p + 3b = 23

The perimeter of a rectangular volleyball court is 180 feet. The court’s width, w, is half its length, l. Which system of linear equations could be used to determine the dimensions, in feet, of the volleyball court? 2L + 2W = 180 W = ½L