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Do Now 12/12/18

Do Now 12/12/18. Take out HW from last night. Text p. 245, #9-18 all, 20 & 27 Copy HW in your planner. Text p. 251, #4-22 evens, 31

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Do Now 12/12/18

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  1. Do Now 12/12/18 • Take out HW from last night. • Text p. 245, #9-18 all, 20 & 27 • Copy HW in your planner. • Text p. 251, #4-22 evens, 31 • In your notebook, answer the following question. A farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represents this situation. How many acres of each crop should the former plant? x = y =

  2. A farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represents this situation. How many acres of each crop should the farmer plant? x + y = 180 x = x = 3y y =

  3. HomeworkText p. 245, #9-18 all, 20 & 27

  4. HomeworkText p. 245, #9-18 all, 20 & 27

  5. Learning Goal • Students will be able to write and graph systems of linear equations. Learning Target • Students will be able to solve systems of linear equations by elimination

  6. Section 5.1“Solve Linear Systems by Graphing” Linear System– consists of two more linear equations. x + 2y = 7 Equation 1 3x – 2y = 5 Equation 2 A solution to a linear system is an ordered pair (a point) where the two linear equations (lines) intersect (cross).

  7. Section 5.2“Solve Linear Systems by Substitution”

  8. “Solve Linear Systems by Substituting” Equation 1 x – 2y = -6 x = -6 + 2y Equation 2 4x + 6y = 4 4x + 6y = 4 4(-6 + 2y)+ 6y = 4 Substitute -24 + 8y + 6y = 4 -24 + 14y = 4 y = 2 x – 2y = -6 Equation 1 Substitute value for x into the original equation x = -6 + 2(2) x = -2 (-2) - 2(2) = -6 -6 = -6 4(-2) + 6(2) = 4 4 = 4 The solution is the point (-2,2). Substitute (-2,2) into both equations to check.

  9. During a football game, a bag of popcorn sells for $2.50 and a pretzel sells for $2.00. The total amount of money collected during the game was $336. Twice as many bags of popcorn sold compared to pretzels. How many bags of popcorn and pretzels were sold during the game? y = 2x x = $2.50y + $2.00x = $336 y = 96 bags of popcorn and 48 pretzels

  10. “How Do You Solve a Linear System???” (1) Solve Linear Systems by Graphing (5.1) (2) Solve Linear Systems by Substitution (5.2) (3) Solve Linear Systems by ELIMINATION!!! (5.3)

  11. Section 5.3 “Solve Linear Systems by Elimination” • ELIMINATION- adding or subtracting equations to obtain a new equation in one variable.

  12. “Solve Linear Systems by Elimination” ADDITION Eliminated 2x + 3y = 11 Equation 1 + -2x + 5y = 13 Equation 2 8y = 24 y = 3 2x + 3y = 11 Equation 1 Substitute value for y into either of the original equations 2x + 3(3) = 11 2x + 9 = 11 x = 1 2(1) + 3(3) = 11 11 = 11 -2(1) + 5(3) = 13 13 = 13 The solution is the point (1,3). Substitute (1,3) into both equations to check.

  13. “Solve Linear Systems by Elimination” Eliminated SUBTRACTION 4x + 3y = 2 Equation 1 _ + -5x + -3y = 2 5x + 3y = -2 Equation 2 -x = 4 x = -4 4x + 3y = 2 Equation 1 Substitute value for x into either of the original equations 4(-4) + 3y = 2 -16 + 3y = 2 y = 6 4(-4) + 3(6) = 2 2 = 2 5(-4) + 3(6) = -2 -2 = -2 The solution is the point (-4,6). Substitute (-4,6) into both equations to check.

  14. “Solve Linear Systems by Elimination” Eliminated 8x - 4y = -4 Equation 1 Arrange like terms + -3x + 4y = 14 4y = 3x + 14 Equation 2 5x = 10 x = 2 8x - 4y = -4 Equation 1 Substitute value for x into either of the original equations 8(2) - 4y = -4 16 - 4y = -4 y = 5 8(2) - 4(5) = -2 -2 = -2 4(5) = 3(2) + 14 20 = 20 The solution is the point (2,5). Substitute (2,5) into both equations to check.

  15. 4x – 3y = 5 -2x + 3y = -7 7x – 2y = 5 7x – 3y = 4 On Your Own 3x + 4y = -6 2y = 3x + 6 (-1, -3) (1,1) (-2,0)

  16. “Solve Linear Systems by Elimination Multiplying First!!” Multiply First Eliminated 6x + 5y = 19 6x + 5y = 19 Equation 1 x (-3) + -6x – 9y = -15 2x + 3y = 5 Equation 2 -4y = 4 y = -1 2x + 3y = 5 Equation 2 Substitute value for y into either of the original equations 2x + 3(-1) = 5 2x - 3 = 5 x = 4 6(4) + 5(-1) = 19 19 = 19 2(4) + 3(-1) = 5 5 = 5 The solution is the point (4,-1). Substitute (4,-1) into both equations to check.

  17. “Solve Linear Systems by Elimination Multiplying First!!” Multiply First Eliminated x (-2) 2x + 5y = 3 -4x - 10y = -6 Equation 1 + 3x + 10y = -3 3x + 10y = -3 Equation 2 -x = -9 x = 9 2x + 5y = 3 Equation 1 Substitute value for x into either of the original equations 2(9) + 5y = 3 18 + 5y = 3 y = -3 2(9) + 5(-3) = 3 3 = 3 3(9) + 10(-3) = -3 -3 = -3 The solution is the point (9,-3). Substitute (9,-3) into both equations to check.

  18. “Solve Linear Systems by Elimination Multiplying First!!” Multiply First Eliminated x (2) 4x + 5y = 35 8x + 10y = 70 Equation 1 + x (-5) 15x - 10y = 45 -3x + 2y = -9 Equation 2 23x = 115 x = 5 4x + 5y = 35 Equation 1 Substitute value for x into either of the original equations 4(5) + 5y = 35 20 + 5y = 35 y = 3 4(5) + 5(3) = 35 35 = 35 -3(5) + 2(3) = -9 -9 = -9 The solution is the point (5,3). Substitute (5,3) into both equations to check.

  19. “Solve Linear Systems by Elimination Multiplying First!!” Multiply First Eliminated x (2) 9x + 2y = 39 18x + 4y = 78 Equation 1 + x (-3) -18x - 39y = 27 6x + 13y = -9 Equation 2 -35y = 105 y = -3 9x + 2y = 39 Equation 1 Substitute value for y into either of the original equations 9x + 2(-3) = 39 9x - 6 = 39 x = 5 9(5) + 2(-3) = 39 39 = 39 6(5) + 13(-3) = -9 -9 = -9 The solution is the point (5,-3). Substitute (5,-3) into both equations to check.

  20. x + y = 2 2x + 7y = 9 6x – 2y = 1 -2x + 3y = -5 Guided Practice (1,1) (-0.5, -2) 3x - 7y = 5 9y = 5x + 5 (-10,-5)

  21. A business with two locations buys seven large delivery vans and five small delivery vans. Location A receives five large vans and two small vans for a total cost of $235,000. Location B receives two large vans and three small vans for a total cost of $160,000. What is the cost of each type of van? 2x + 5y = 235,000 x = 3x + 2y = 160,000 y = (30,000, 35,000) $30,000 for a small van and $35,000 for a large van.

  22. Homework PARCC prep • Text p. 251, #4-22 evens, 31

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