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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

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3.2 Solving Systems Algebraically

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  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.

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