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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 709 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.3x − 2y = 0 and 4x + 4y = −20 →
  2. 2.4x + y = −24 and x + 4y = 9 →
  3. 3.5x + 4y = 39 and 3x + 6y = 27 →
  4. 4.3x + y = −7 and x − 2y = 0 →
  5. 5.5x + 2y = −19 and 2x + 5y = 5 →
  6. 6.4x − y = −36 and 3x − 5y = −61 →
  7. 7.5x + 2y = 63 and x − 2y = −9 →
  8. 8.5x + 4y = 63 and 4x + 5y = 63 →
  9. 9.6x + 5y = −17 and 5x + 6y = −5 →
  10. 10.3x + 2y = 36 and 6x − 6y = −18 →
  11. 11.3x + 6y = 6 and 6x + 3y = −33 →
  12. 12.6x + 2y = 58 and 4x + 5y = 68 →
  13. 13.6x + 6y = −60 and 6x − 4y = −50 →
  14. 14.6x + 5y = 54 and 6x − 5y = −6 →
  15. 15.5x + y = −36 and 5x + 5y = −20 →
  16. 16.x + 2y = 7 and x + 5y = 10 →
  17. 17.8x + 2y = 44 and 2x + 8y = 26 →
  18. 18.x + y = −6 and 3x + 4y = −27 →
  19. 19.2x + 7y = −9 and 7x + 2y = −54 →
  20. 20.2x + 6y = 20 and x − 3y = −2 →
  21. 21.6x + 3y = 27 and 3x + 6y = 45 →
  22. 22.6x + 2y = 0 and 5x − 5y = −60 →
  23. 23.7x + 4y = 53 and 4x + 7y = 68 →
  24. 24.3x − 4y = 6 and 2x − 4y = 8 →
  25. 25.4x + 2y = −4 and 5x − 2y = 13 →
  26. 26.6x − y = 21 and 6x + 6y = 84 →
  27. 27.4x + 5y = −14 and 2x − 5y = 38 →
  28. 28.4x + 6y = 50 and 4x − 6y = 14 →
  29. 29.6x + 3y = −30 and 6x − 5y = 18 →
  30. 30.2x + 4y = 10 and 4x + 2y = 14 →
  31. 31.x + 6y = 33 and 6x + 4y = 70 →
  32. 32.8x + 2y = 42 and 2x + 8y = 18 →
  33. 33.3x + 7y = 56 and 7x + 3y = 64 →
  34. 34.x − y = 0 and 2x + 6y = 72 →
  35. 35.7x + 6y = −21 and 6x + 7y = −5 →
  36. 36.3x + 4y = 39 and 4x + 3y = 31 →
  37. 37.4x + 3y = −11 and 2x − 5y = 53 →
  38. 38.6x − 4y = 40 and 3x + 6y = 36 →
  39. 39.9x + 5y = −30 and 5x + 9y = 2 →
  40. 40.2x + 3y = 3 and 2x + 5y = 17 →

Answer key

  1. x = −2, y = −3
  2. x = −7, y = 4
  3. x = 7, y = 1
  4. x = −2, y = −1
  5. x = −5, y = 3
  6. x = −7, y = 8
  7. x = 9, y = 9
  8. x = 7, y = 7
  9. x = −7, y = 5
  10. x = 6, y = 9
  11. x = −8, y = 5
  12. x = 7, y = 8
  13. x = −9, y = −1
  14. x = 4, y = 6
  15. x = −8, y = 4
  16. x = 5, y = 1
  17. x = 5, y = 2
  18. x = 3, y = −9
  19. x = −8, y = 1
  20. x = 4, y = 2
  21. x = 1, y = 7
  22. x = −3, y = 9
  23. x = 3, y = 8
  24. x = −2, y = −3
  25. x = 1, y = −4
  26. x = 5, y = 9
  27. x = 4, y = −6
  28. x = 8, y = 3
  29. x = −2, y = −6
  30. x = 3, y = 1
  31. x = 9, y = 4
  32. x = 5, y = 1
  33. x = 7, y = 5
  34. x = 9, y = 9
  35. x = −9, y = 7
  36. x = 1, y = 9
  37. x = 4, y = −9
  38. x = 8, y = 2
  39. x = −5, y = 3
  40. x = −9, y = 7

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