2. 1 Simultaneous Equations MENU Algebra Menu Ducks & Sheep Linear Type : 4x + 2y = 20 Teacher examples 4x – y = 8 Linear Type : 4x + 2y = 20 Questions 4x – y = 8 Linear Type : 3x + 2y = 14 Teacher examples 4x +5y = 28 Linear Type : 3x + 2y = 14 Questions 4x + 5y = 28 Linear Type : 2x + 4y = 10 Teacher examples 3x = 6 + 2y Linear Type : 2x + 4y = 10 Questions 3x = 6 + 2y Non - Linear. Teacher examples Notes on Teacher Examples Non - Linear. Questions

3. 2 Notes on Teacher Examples Teacher example questions have been left blank and animation free due to the sheer variety of approaches used by pupils to solve the problems. The teacher can work through the problems either by using the interactive pens if available or simply use a whiteboard pen on a normal whiteboard. Menu

4. 3 There are some ducks and some sheep on a farm. Altogether they have 35 heads and 94 feet. How many ducks ? How many sheep ? 23 duck s 12 sheep Menu

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6. 5 Example 1 4x + 2y = 20 4x – y = 8 Menu

7. 6 Example 2 3x + 2y = 13 3x + 5y = 28 Menu

8. 7 Example 3 4x + 3y = 17 2x + 3y = 13 Menu

9. 8 Example 4 6x + 2y = 12 5x - 2y = - 1 Menu

10. 9 Example 5 2x - y = 11 3x + y = 29 Menu

11. 10 3x + 2y = 11 5x – 2y = 13 a + b = 7 3a – b = 1 2x – y = 4 -2x + 3y = -8 5p + 4q = 13 3p + 4q = 7 2a + 5b = 11 2a + 7b = 17 5x - 2y = 0 3x - 2y = -2 5a - 4b = -12 2a – 4b = 0 3x + 2y = -1 4x + 2y = -1 5x – 3y = 41 4x + 3y = 22 3p + q = 9 2p + q = 5 1 2 3 4 5 6 7 8 9 10 x= 3 y = 1 x = 1 y = -2 a = 2 b = 5 p = 3 q = -0.5 a = -2 b = 3 x = 1 y = 2.5 a = -4 b = -2 x = 0 y = -0.5 x = 7 y = -2 p = 4 q = -3 Menu Answers

12. 11 Example 1 3x + 2y = 14 4x + 5y = 28 Menu

13. 12 Example 2 4x + 3y = 18 x - 5y = 16 Menu

14. 13 Example 3 3x - 5y = 19 8x - 3y = - 1 Menu

15. 14 2a + 3d = 18 3a – 4d = -7 2x – 4y = 18 4x + 3y = 14 4p – 5q = 41 3p – 4q = 32 2x + 3y = 7 3x + 6y = 15 3a – 8b = -5 5a – 4b = -13 3x + 2y = 8 2x + 3y = 2 3a + 5b = -4 5a – 2b = -17 2x + 3y = -11 -6x + 8y =-35 8p – 6q = 56 6p + 4q = -9 2x – 3y = 9 3x + 4y = -29 1 2 3 4 5 6 7 8 9 10 a = 3 d = 4 p = 4 q = -5 x = 5 y = -2 x = -1 y = 3 a = -3 b = -0.5 x = 4 y = -2 a = -3 b = 1 x = 0.5 y = -4 p = 2.5 q = -6 x = -3 y = -5 Menu Answers

16. 15 Example 1 2x + 4y = 10 3x = 6 + 2y Menu

17. 16 Example 2 3x = 7 + y 5y = 5 – 5x Menu

18. 17 Example 3 3x + y + 7 = 0 2y = 4x - 10 Menu

19. 18 Example 4 4x + 3y = 23 3y – 6x = - 27 Menu

20. 19 3x + 2y = 5 3y – x = 13 y = x + 2 y + x = -6 2x + y = 3 x = y + 3 2x - y - 2 = 0 4x + 3y = 24 4x + 3y = -10 2y + 3x = -7 3a = 14 – 5b 2b = 4a - 10 x – y = 1 y = 2x - 2 1 2 3 4 5 6 7 x = -1 y = 4 x = 2 y = -1 x = -4 y = -2 x = 3 y = 4 x = -1 y = -2 a = 3 b = 1 x = 1 y = 0 Menu Answers

21. 20 Menu

22. 21 Teacher Example 1 : x - y = 3 x + y 2 = 5 Menu

23. 22 Teacher Example 2 : x - y = 2 x 2 + y 2 = 10 Menu

24. 23 Teacher Example 3 : 2x + y = 2 xy + 4 = 0 Menu

25. 24 1)2x 2 + y 2 = 17 2)x – y = 43)x 2 + y = 4 2x – y = 1 x – 2y 2 = 3x + y = 4 4)x y = 10 5)3x + y = 46)2x – y = 1 x – 2y = 1x y = 1x + y – x y = - 17 7)x – 3y + 2 = 0 8)x 2 – 9y 2 = 279)2x – y = 1 x y – y 2 = 4x + 3y = 34x 2 – y 2 = 7 10)y = x – 3 11)y = 2x 2 + 3x + 412)x y = 12 y = x 2 – 3x – 3 y = x + 82x – y = 3 Solve the following Simultaneous Equations : x = 2, y = 3 x = - 1/3, y = - 3 2/3 x = 5, y = 1 x = 3 1/2, y = - 1/2 x = 0, y = 4 x = 1, y = 3 x = 5, y = 2 x = - 4, y = - 2 1/2 x = 1, y = 1 x = 1/3, y = 3 x = 4, y = 7 x = - 2, y = - 5 x = 4, y = 2 x = - 5, y = - 1 x = 6 y = - 1 x = 2 y = 3 x = 0, y = - 3 x = 4, y = 1 x = 1, y = 9 x = - 2, y = 6 x = 2 1/2, y = 2 x = - 1, y = - 5 Menu Answers

26. 25 End of Simultaneous Equations Presentation. Return to previous slide.