EQ WHY CAN IT BE HELPFUL TO SOLVE

EQ: WHY CAN IT BE HELPFUL TO SOLVE A SYSTEM OF EQUATIONS? TOPIC: SOLVING SYSTEM OF EQUATIONS THROUGH ELIMINATION � Solve the equation 2 x + 8 + 7 y = 3 x + 7 y � Graph � Y= 2 x + 3

ANSWERS � Solve the equation 2 x + 8 + 7 y = 3 x + 7 y -7 y 2 x + 8 = 3 x -2 x 8=x � Graph � Y= 2 x + 3 x -1 0 1 y 1 3 5

� SWBAT solve systems of equations using elimination and apply to real world situations. � Given 1 MC and 2 real world situations, students will solve systems of equations using elimination with 80% accuracy. � 2. 4. d. i Objective DOL

� You and a friend go to Taco Bell for lunch. You order three soft tacos and three burritos and your bill totals $11. 25. Your friend’s bill is $12. 50 for four soft tacos and three burritos. How much do soft tacos cost? How much do burritos cost? � x = the cost of soft tacos � y = the cost of burritos

� To remove or get rid of � In this case we are trying to get rid of one of our variables by making it 0 � Hold up one finger for “+” or two fingers for “-” card for how we would make these two numbers 0 -3 and 3 2 and 2 -4 and -4 6 and -6 8 and 8

1. Write your equations (read through the problem, highlight important information, define your variables) 2. Write the equations on top of each other 3. Decide to add or subtract the two equations (pick the operation that will cancel out one of the variables) 4. Solve for the remaining variable 5. Plug the found value into one of the original equations and solve for the remaining variable 6. Answer the question

Practice Set- Whiteboards n Solve each set of system of equations 3 x – 2 y = 13 x + 2 y = 7

Practice Set n Solve each set of system of equations 3 x – 2 y = 13 x + 2 y = 7 4 x = 20 (5, 1) x=5 5 + 2 y = 7 -5 -5 2 y = 2 y=1

Practice Set- Whiteboards n Solve each set of system of equations -4 x + 2 y = 8 4 x – 3 y = -10

Practice Set n Solve each set of system of equations -4 x + 2 y = 8 4 x – 3 y = -10 -y = -2 y=2 -4 x +2(2) = 8 -4 x + 4 = 8 -4 -4 -4 x = 4 x = -1 (-1, 2)

�A youth group and their leaders visited Cave of the Winds. Two adults and five students in one van paid $77 for the Grand Avenue Tour of the cave. Two adults and seven students in a second van paid $95 for the same tour. Find the adult price and student price of the tour. �x = adult price � y = student price � 2 x + 5 y = 77 � 2 x + 7 y = 95 � Y= 9 � X= 16 � Solution: $16 for adult and $9 for students

� You and your partner will have 4 minutes per problem. � This will be completed as a sage and scribe activity. � Person on the right is the sage first (telling) and person on the left is the scribe (doing). � Switch roles for each problem. � There are four total problems. � If you finish a problem early, complete the problems on the powerpoint for extra credit.

� Jayce bought 2 bath towels and returned 3 hand towels. His sister Jayna bought 3 bath towels and 3 hand towels. Jayce’s bill was $5. Jayna’s bill was $45. What are the prices of a bath towel and a hand towel? �x = cost of bath towel � y = cost of hand towel � 2 x – 3 y = 5 � 3 x + 3 y = 45 � (10, 5) � $10 for a bath towel � $5 for a hand towel

� The Lees spent $31 on movie tickets for 2 adults and 3 children. The Macias spent $26 on movie tickets for 2 adults and 2 children. What are the prices for adult and children movie tickets? x = adult tickets � y = children tickets � � 2 x + 3 y = 31 � 2 x + 2 y = 26 � (8, 5) � $8 for adults � $5 for children

� Mr. Smith bought a package of 3 chicken legs and a package of 7 chicken wings. Mrs. Dawes bought a package of 3 chicken legs and a package of 5 chicken wings. Mr. Smith bought 45 ounces of chicken while Mrs. Dawes bought 39 ounces of chicken. How much did each leg and wing weigh? �x = weight of a chicken leg � y = weight of a chicken wing � 3 x + 7 y = 45 � 3 x + 5 y = 39 � (8, 3) � 8 oz chicken leg � 3 oz chicken wing

� Last month Stephanie spent $57 on 4 allergy shots and 1 office visit. This month she spent $9 after 1 office visit and a refund for 2 allergy shots from her insurance company. How much does an office visit cost? An allergy shot? �x = cost of an office visit � y = cost of an allergy shot �x + 4 y = 57 � x – 2 y = 9 � (25, 8) � $25 for an office visit � $8 for an allergy shot

� All 28 members in Crestview High School’s Ski Club went on a one-day ski trip. Members can rent skis for $16 per day or snowboards for $19 per day. The club paid a total of $478 for rental equipment. How many members rented skis and how many rented snowboards? � x = # renting snowboards; y = # renting skis � x + y = 28 � 16 + 19 y = 478 � x = 18 rented skis � y = 10 rented snowboards

� You have 13 total movies at your house. There is a combination of DVD’s and Blue. Rays. The DVD’s are worth 7 dollars and the Blue. Rays are worth 13 dollars. If you have a total value of 127 dollars, how many of each do you have? x + y = 13 7 x + 13 y = 127 -7 x -7 y = -91 7 x + 13 y = 127 6 y = 36 Y=6 x + 6= 13 x=7 Solution (DVD 7, Blue Ray 6)

Helps us determine values for unknown variables when there is more than one. Can be helpful when comparing cell phone plans, health care plans, etc. Especially helpful in business to find break even points

� a) add the two equations � b) subtract the two equations � c) multiply the top equation by 2 � d) multiply the bottom equation by 2

� You and a friend go to Taco Bell for lunch. You order three soft tacos and three burritos and your bill totals $11. 25. Your friend’s bill is $12. 50 for four soft tacos and three burritos. How much do soft tacos � cost? How much do burritos cost? � X= the cost of soft tacos � Y= the cost of burritos � 3 x + 3 y = 11. 25 � 4 x + 3 y = 12. 50

� At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43. Tori bought two pairs of gloves and two hats for $30. What were the prices for the gloves and hats? � x = price of gloves � y = price of hats � 2 x + 4 y = 43 � 2 x + 2 y = 30

� a) add the two equations � b) subtract the two equations � c) multiply the top equation by 2 � d) multiply the bottom equation by 2

� You and a friend go to Taco Bell for lunch. You order three soft tacos and three burritos and your bill totals $11. 25. Your friend’s bill is $12. 50 for four soft tacos and three burritos. How much do soft tacos � cost? How much do burritos cost? � X= the cost of soft tacos � Y= the cost of burritos � 3 x + 3 y = 11. 25 � 4 x + 3 y = 12. 50 (1. 25, 2. 50)

� At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43. Tori bought two pairs of gloves and two hats for $30. What were the prices for the gloves and hats? � x = price of gloves � y = price of hats � 2 x + 4 y = 43 � 2 x + 2 y = 30 (8. 50, 6. 50)