1 / 16

3.2 Solving Systems Algebraically

3.2 Solving Systems Algebraically. *Substitution *Elimination . Solving using Substitution. Solve for one of the variables in one of the equations with a coefficient of 1 Substitute the expression into the other equation Solve the equation

cedric
Télécharger la présentation

3.2 Solving Systems Algebraically

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. 3.2 Solving Systems Algebraically *Substitution *Elimination

  2. Solving using Substitution • Solve for one of the variables • in one of the equations • with a coefficient of 1 • Substitute the expression into the other equation • Solve the equation • Plug answer back into the original equation to find the other variable • Write your two answers together as an ordered pair

  3. Examples • 4x + 3y = 4 2x – y + 7 • 2x – 3y = 6 x + y = -12

  4. Practice!! 1) 3x – y = 0 4x + 3y = 26 2) 2x + 3y = 12 -2x + 4y = 9

  5. Warm-up • Solve by Substitution • 1. y = x + 4 • y = 3x • 2. y = x – 7 • 2x + y = 8 • ( 1, 1 ) ( 5 , -2 )

  6. Solving using Elimination • Get one set of variables coefficients to be equal but opposite (ex. 3 and -3) • Using multiplication • Add the two equations together vertically • Solve for the remaining variable • Plug answer back into the original equation to get the other variable • Write your two answers together as an ordered pair

  7. What if the variables both cancel out? • If both variables are eliminated • -and you get a true statement they are the same line and there are infinite solutions. • -and you get a false statement the lines are parallel and there are no solutions.

  8. Mike and Caryn bought some pens and pencils. Mike bought 4 pens and 5 pencils, which cost him $6.71. Caryn bought 5 pens and 3 pencils, which cost her $7.12. Write a system of equations and solve to determine the price of each pen and pencil.

  9. You have just enough money to buy a loaf of bread for $1.95. You have 12 coins, all quarters and dimes. Write and solve a system of equations to determine how many of each type of coin you have.

  10. Revenue – Expenses = Profit

  11. Suppose you are starting an office cleaning service. You have spent $315 on equipment. To clean each office, you use $4 worth of supplies. You charge $25 per office. How many Offices must you clean to break even? 15 offices

  12. Identify variables! Write and solve a system • Suppose you bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later, you bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much did each party hat cost? • streamers$2.50/hats$1.50

  13. Examples 2x – y = 3 -2x + y = -3 2x – 3y = 18 -2x + 3y = -6 4x – 2y = 7 x + 2y = 3 4x + 9y = 1 4x + 6y = -2 2x + 4y = -4 3x + 5y = -3

  14. Practice!!!! 1) -3x + 5y = 6 6x – 10y = 0 2) 3x + y = -9 -3x – 2y = 12 -3x + 5y = 7 6x – 10y = -14 4) 5x – 2y = -19 2x + 3y = 0

  15. Warm up • Solve the following systems by elimination. • ( 2, -1 ) ( 2, 0 ) (1/2, 2 )

  16. Three pizzas and four sandwiches cost $34. Three pizzas and seven sandwiches cost $41.50. How much does a pizza cost? Identify variables, write and solve a system of equations.

More Related