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Write all possible solutions:

Two integers have a sum of 14. The larger number is equal to 2 more than twice the smaller number. Write all possible solutions:. Two integers with a sum of 14. (write smaller integer first). _ and __ _ and __ _ and __ _ and __. 4 10. _ and __ _ and __

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Write all possible solutions:

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  1. Two integers have a sum of 14. The larger number is equal to 2 more than twice the smaller number.

  2. Write all possible solutions: Two integers with a sum of 14. (write smaller integer first) _ and __ _ and __ _ and __ _ and __ 4 10 _ and __ _ and __ _ and __ _ and __ 0 14 5 9 1 13 6 8 2 12 7 7 3 11 x + y = 14 Equation:

  3. The larger number is equal to 2 more than twice the smaller number. 2 2 y = __x + __ Equation: m b (0, 14) (1, 13) (2, 12) (3, 11) (4, 10) (5, 9) (6, 8) (7, 7) larger number smaller number What works? y = 2x + 2 10 4 (___) = 2(___) + 2 10 = 8 + 2 10 = 10 (4, 10)

  4. Lets Graph! y 15 14 13 x + y = 14 y = 2x + 2 12 11 y = -x + 14 10 9 8 larger number 7 6 5 4 3 2 1 x ( , ) 4 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 smaller number

  5. System of Equations: Two or more equations with the same set of variables. x + y = 14 y = 2x + 2 (4, 10) 10 = 2(4) + 2 10 = 8 + 2 10 = 10 4 + 10 = 14 14 = 14

  6. Solving systems of equations by graphing: Step 1) Step 2) Step 3) Step 4) Get both equations in slope-intercept form. Graph both equations. Find the point where the lines intersect. Check the point in bothoriginal equations. [ y = mx + b ]

  7. Solve the system y = -2x - 3 and y = 2x + 5 by graphing. (-2, 1)

  8. Solve the system y = x - 1 and y = 2x - 2 by graphing. ( , ) 1 0

  9. Solve the system y = 4x and y = x + 3 by graphing. (1, 4)

  10. Solve the system y = 4x - 2 and y = -3x + 5 by graphing. (1, 2)

  11. Greg's Motorsports has motorcycles (2 wheels) and ATV's (4 wheels) in stock. The store has a total of 45 vehicles, that have a total of 130 wheels. Write a system of equations to represent the situation. y = number of motorcycles x = number of ATV's 75 60 45 45 total vehicles: Number of Motorcycles x + y = 45 30 15 x-int: 45 y-int: 45 130 total tires: 4x + 2y = 130 Number of ATVs (20, 25) (number of motorcycles) (number of ATVs) (2 tires on each motorcycle) (4 tires on each ATV) y-int: 65 x-int: 32.5

  12. Creative Crafts gives scrapbooking lessons for $15 per hour plus a $10 supply charge. Scrapbooks Incorporated gives lessons for $20 per hour with no additional charges. Write a system of equations that represents the situation. y = total cost x = number of hours Creative Crafts 15x + 10 = y 2 x-int: - y-int: 10 3 (slope = 15) Scrapbooks Inc. 20x = y (2, 40) x-int: 0 y-int: 0 (slope = 20)

  13. The sum of Sally's age plus twice Tom's age is 12. The difference between Sally's age and Tom's age is 3. Write and solve a system of equations to find their ages. y = Sally's age x = Tom's age The sum of Sally's age and twice Tom's age is 12: y + 2x = 12 x-int: 12 y-int:6 The difference between Sally's age & Tom's age is 3: y - x = 3 x-int: -3 y-int:3 (3, 6)

  14. A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there? 20 18 16 14 12 10 8 6 4 2 y = number of pigs x = number of ducks Total of 10 animals: number of pigs x + y = 10 x-int: 10 y-int: 10 Total of 36 legs: 2 4 6 8 10 12 14 16 18 20 number of ducks 2x + 4y = 36 (2, 8) x-int: 18 y-int: 9

  15. A system of equations consists of two lines. One line passes through (2, 3) and (0, 5). The other line passes through (1, 1) and (0, -1). Determine if the system has no solutions, one solution, or an infinite number of solutions. y2 - y1 y2 - y1 m = m = x2 - x1 x2 - x1 1 - (-1) 3 - 5 m = m = 1 - 0 2 - 0 2 -2 m = = 2 m = = -2 1 2 y-intercept: y-intercept: 5 -1 Equation: Equation: y = 2x - 1 y = -2x + 5 different slope, different y-intercept One Solution (2, 3)

  16. A system of equations consists of two lines. One line passes through (2, 3) and (0, 5). The other line passes through (1, 1) and (0, -1). Determine if the system has no solutions, one solution, or an infinite number of solutions. y2 - y1 y2 - y1 m = m = x2 - x1 x2 - x1 1 - (-1) 3 - 5 m = m = 1 - 0 2 - 0 2 -2 m = = 2 m = = -2 1 2 y-intercept: y-intercept: 5 -1 Equation: Equation: y = 2x - 1 y = -2x + 5 different slope, different y-intercept One Solution (2, 3)

  17. A system of equations consists of two lines. One line passes through (-1, 3) and (0, 1). The other line passes through (1, 4) and (0, 2). Determine if the system has no solutions, one solution, or an infinite number of solutions. y2 - y1 y2 - y1 m = m = x2 - x1 x2 - x1 4 - 0 3 - 1 m = m = 1 - 2 -1 - 0 different slope, 4 2 m = = -4 m = = -2 different y-intercept -1 -1 One Solution y-intercept: y-intercept: 4 2 Equation: Equation: y = -4x + 2 y = -2x + 4

  18. Number of Solutions: If the lines intersect, there is 1 solution. (different slope, different y-intercept) If the lines are parallel, there are no solutions. (same slope, different y-intercept) If the lines are the same, there are an infinite number of solutions. (same slope, same y-intercept)

  19. Solve the system y = 2x + 1 and y = 2x - 3 by graphing. same slope, different y-intercept - No Solutions

  20. Solve the system of equations by graphing. y - x = 1 y = x - 2 + 3 y = x + 1 + x + x y = x + 1 same slope, same y-intercept -Infinite Number of Solutions

  21. Solve the system of equations by graphing. y = 2x +1 y - 3 = 2x + 1 + 3 + 3 y = 2x + 4 same slope, different y-intercept - No Solutions

  22. Homework: Page 239, #1-5, 7-10

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