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Do Now 1/10/11

Do Now 1/10/11. Copy HW in your planner. Text p. 430, #4-20 evens, 30-34 evens Text p. 439, #4-24 even, #32, #36 Open your textbook to page 424 and preview Chapter 7 “Systems of Equations and Inequalities”. Chapter 7 Preview “Solving and Graphing Linear Systems”.

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Do Now 1/10/11

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  1. Do Now 1/10/11 • Copy HW in your planner. • Text p. 430, #4-20 evens, 30-34 evens • Text p. 439, #4-24 even, #32, #36 • Open your textbook to page 424 and preview Chapter 7 “Systems of Equations and Inequalities”

  2. Chapter 7 Preview “Solving and Graphing Linear Systems” (7.1) Solve Linear Systems by Graphing (7.2) Solve Linear Systems by Substituting (7.3) Solve Linear Systems by Adding or Subtracting (7.4) Solve Linear Systems by Multiplying First (7.5) Solve Special Types of Linear Systems (7.6) Solve Systems of Linear Inequalities

  3. Section 7.1“Solve Linear Systems by Graphing” Linear System– consists of two or 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).

  4. 7 = 7 5 3(3)–2(2) 5 = 5 ? ? = = 3+ 2(2) 7 Using a Graph to Solve a Linear System Use the graph to solve the system. Then check your solution algebraically. Equation 1 x + 2y = 7 Equation2 3x – 2y = 5 SOLUTION The lines appear to intersect at the point (3, 2). CHECK Substitute3forxand2foryin each equation. Equation 1 Equation2 Because the ordered pair (3, 2) is a solution of each equation, it is a solution of the system. x+2y=7 3x–2y=5

  5. -7 -4+(-3) -7= -7 ? ? = = 4+ 4(-3) -8 Using a Graph to Solve a Linear System Use the graph to solve the system. Then check your solution algebraically. Equation 1 x + 4y = -8 Equation2 -x +y = -7 SOLUTION The lines appear to intersect at the point (4, -3). CHECK Substitute 4 forxand -3 foryin each equation. Equation 1 Equation2 Because the ordered pair (4, -3) is a solution of each equation, it is a solution of the system. x+4y=-8 -x+y=-7 -8 = -8

  6. A B y = 4x y = 4x y = 90 + 13x y = 13x D C y = 13x y = 90 + 4x y = 90 + 4x y = 90 + 13x Standardized Test Practice The parks and recreation department in your town offers a season pass for $90. As a season pass holder, you pay $4 per session to use the town’s tennis courts. Without the season pass, you pay $13 per session to use the tennis courts. Which system of equations can be used to find the number xof sessions of tennis after which the total cost ywith a season pass, including the cost of the pass, is the same as the total cost without a season pass?

  7. y = 90+ 4x A B y = 4x y = 4x y = 90 + 13x y = 13x y=13x D C y = 13x y = 90 + 4x y = 90 + 4x y = 90 + 13x Standardized Test Practice Which system of equations can be used to find the number xof sessions of tennis after which the total cost ywith a season pass, including the cost of the pass, is the same as the total cost without a season pass? EQUATION1 EQUATION2

  8. Solve a multi-step problem A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented. STEP1 Write a linear system. Let xbe the number of pairs of skates rented, and let ybe the number of bicycles rented. x + y =25 Equation for number of rentals 15x + 30y = 450 Equation for money collected from rentals

  9. ANSWER The business rented 20 pairs of skates and 5 bicycles. ? ? 15(20)+30(5) 450 20+525 = = 450 =450 25 =25 Solve a multi-step problem STEP2 Graph both equations. STEP3 Estimate the point of intersection. The two lines appear to intersect at(20, 5). STEP4 Check whether (20, 5) is a solution.

  10. Section 7.2“Solve Linear Systems by Substitution”

  11. “Solve Linear Systems by Substituting” y = 3x + 2 Equation 1 Equation 2 x + 2y = 11 x + 2y = 11 x + 2(3x + 2) = 11 Substitute x + 6x + 4 = 11 7x + 4 = 11 x = 1 y = 3x + 2 Equation 1 Substitute value for x into the original equation y = 3(1) + 2 y = 5 (5) = 3(1) + 2 5 = 5 (1) + 2(5) = 11 11 = 11 The solution is the point (1,5). Substitute (1,5) into both equations to check.

  12. “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.

  13. Solve a multi-step problem A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented. STEP1 Write a linear system. Let xbe the number of pairs of skates rented, and let ybe the number of bicycles rented. x + y =25 Equation for number of rentals 15x + 30y = 450 Equation for money collected from rentals

  14. ANSWER The business rented 20 pairs of skates and 5 bicycles. Solve a multi-step problem STEP2 Solve equation 1 for x. Equation 1 x + y = 25 x = 25 - y Equation 2 15x + 30y = 450 Substitute 15(25 - y) + 30y = 450 15x + 30y = 450 375 - 15y + 30y = 450 375 + 15y = 450 15y = 75 y = 5 x + y = 25 Equation 1 Substitute value for x into the original equation x + (5) = 25 x = 20

  15. 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

  16. Homework NJASK7 prep • Text p. 430, #4-20, 30-34 evens • Text p. 439, #4-24 even, #32, #36

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