1 / 16

Solving Systems of Equations by Substitution and Elimination

Learn how to solve systems of equations using the substitution and elimination methods. This includes isolating variables, using coefficients, and graphing. Follow step-by-step examples and check your solutions. Also, discover the best method for different types of equations.

morganbrown
Download Presentation

Solving Systems of Equations by Substitution and Elimination

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm up • Solve the given system by substitution: • 2x – y = 7 • 3x + 3y = - 3 • Solve the given system by elimination: • 2) -3x + 4y = -4 • 3x – 6y = 6

  2. Summary of Methods • Substitution: Requires that one of the variables be isolated on one side of the equation. It is especially convenient when one of the variables has a coefficient of 1 or -1. • Elimination: Can be applied to any system, but it is especially convenient when a variable appears in different equations with coefficients that are opposites. • Graphing: Can provide a useful method for estimating a solution.

  3. Summary of Solving Systems by Westerville South H.S. “All I do is Solve” http://www.schooltube.com/channel/westervillesouthmath/

  4. What is the Best Method for the following? 1. y = 4x – 3 5x – 2y = 6 2. 4x – 5y = 13 2x + 5y = 5

  5. What is the Best Method for the following? 5. 3x – 2y = 6 y = 2x – 4 6. x + y = 4 2x + 3y = 7

  6. CCGPS Coordinate Algebra UNIT QUESTION: How do I justify and solve the solution to a system of equations or inequalities? Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12 Today’s Question: How do I set up word problems involving a system of equations? Standard: MCC9-12.A.REI.6

  7. Solving Word Problems Using Systems

  8. Steps • Define all variables. • Write the system of equations. • Solve using the best method & showing all steps. • State your solution in sentence form. • Check your solution.

  9. 1. You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450. How many of each type of ticket did you sell?

  10. Solve Define variables: S = # of Student Tickets G = # of General Admin Tickets System of equations: S + G = 350 3S + 5G = 1450 G = 200 State your solution(s): S = 150 I sold 200 general admission tickets and 150 student tickets.

  11. 2. Last Saturday Missy bought pants and shirts. Each shirt cost $125 and each pair of pants cost $225. She came home with 26 items and spent exactly $4950. How many pants and shirts did Missy buy?

  12. Solve Define variables: S = # of Shirts P = # of Pants System of equations: S + P = 26 125S + 225G = 4950 P = 17 State your solution(s): S = 9 Missy bought 17 pairs of pants and 9 shirts.

  13. 3. At an Italian bistro, the costs of 2 plates of spaghetti and 1 salad is $27.50. The cost for 4 plates of spaghetti and 3 salads is $59.50. Find the cost of a plate of spaghetti and a salad.

  14. Solve Define variables: P = cost plate of spaghetti S = cost salad System of equations: 2P + S = 27.50 4P + 3S = 59.50 P = 11.50 State your solution(s): S = 4.50 A plate of spaghetti costs $11.50 and a salad costs $4.50.

  15. 4. Peggy walks at a rate of 2 miles per hour and jogs at a rate of 4 miles per hour. She walked and jogged 3.4 miles in 1.2 hours. For how long did Peggy jog and for how long did she walk?

  16. Solve Define variables: W = hours walked J = hours jogged System of equations: W + J = 1.2 2W + 4J = 3.4 W = .7 State your solution(s): J = .5 Peggy walked for 0.7 hours and jogged for 0.5 hours.

More Related