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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 656 · 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. 1.5x + 2y = −9 and 5x + 6y = −37 →
  2. 2.7x + 3y = 13 and 3x + 7y = 57 →
  3. 3.6x + 2y = 40 and 2x + 6y = 8 →
  4. 4.4x + 4y = −8 and 3x − 5y = −46 →
  5. 5.3x + 9y = 27 and 9x + 3y = 33 →
  6. 6.4x + 2y = 2 and 2x + 4y = −2 →
  7. 7.7x + 8y = 89 and 8x + 7y = 91 →
  8. 8.6x + 3y = 60 and 5x − 3y = 17 →
  9. 9.2x − 2y = −22 and 4x − y = −20 →
  10. 10.4x + y = 42 and 3x + 6y = 63 →
  11. 11.2x + y = −1 and x + 2y = −14 →
  12. 12.4x + 3y = −43 and 3x + 4y = −48 →
  13. 13.6x + 2y = −62 and 5x + 4y = −61 →
  14. 14.3x + 2y = −12 and 2x + 3y = −3 →
  15. 15.3x + 7y = 38 and 7x + 3y = −18 →
  16. 16.6x − 5y = −17 and 6x + 4y = 46 →
  17. 17.9x + 7y = 44 and 7x + 9y = 52 →
  18. 18.2x + y = 20 and 5x − 3y = 28 →
  19. 19.2x + 6y = 20 and 6x + y = 26 →
  20. 20.5x + 2y = 22 and 2x + 5y = 34 →
  21. 21.4x + 5y = 19 and 5x + 4y = 26 →
  22. 22.4x − y = −25 and 6x + 3y = −33 →
  23. 23.9x + 8y = 17 and 8x + 9y = 17 →
  24. 24.6x + 5y = 23 and x − 6y = 38 →
  25. 25.4x + 5y = 8 and 5x + 4y = −8 →
  26. 26.2x − 5y = −1 and 2x + 4y = 26 →
  27. 27.4x + 2y = 34 and 2x − 2y = 2 →
  28. 28.2x + 2y = −26 and 2x + 6y = −58 →
  29. 29.x + 5y = −34 and 2x + 2y = −4 →
  30. 30.6x − 5y = 3 and 2x − 6y = −12 →
  31. 31.4x − 4y = −8 and x + 2y = 19 →
  32. 32.6x + y = 22 and x + 6y = −8 →
  33. 33.x − 2y = −27 and x + y = 0 →
  34. 34.4x − 5y = −11 and x + 5y = 41 →
  35. 35.4x + 3y = 36 and 5x − 4y = −17 →
  36. 36.5x + 2y = 43 and 5x + 5y = 55 →
  37. 37.x + 2y = −11 and 6x + 2y = −36 →
  38. 38.6x + 3y = 48 and 3x + 6y = 51 →
  39. 39.9x + 4y = 96 and 4x + 9y = 86 →
  40. 40.6x + 4y = 4 and 4x + 6y = −14 →

Answer key

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

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