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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 237 · 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. 1.4x + 3y = −16 and 3x + 4y = −19 →
  2. 2.3x + 2y = 0 and 2x + 3y = 5 →
  3. 3.6x + 6y = −60 and 4x + 6y = −42 →
  4. 4.x − 4y = 0 and 3x − 6y = −12 →
  5. 5.4x + y = 5 and 5x − 4y = 1 →
  6. 6.8x + 3y = −46 and 3x + 8y = 24 →
  7. 7.6x + 4y = −18 and 4x + 6y = −42 →
  8. 8.3x + 9y = −33 and 9x + 3y = 45 →
  9. 9.x + 4y = 2 and 2x + 5y = 1 →
  10. 10.6x + y = 25 and x − 5y = −32 →
  11. 11.x + 6y = −25 and 6x + y = 25 →
  12. 12.2x + 6y = −58 and x + y = −13 →
  13. 13.9x + y = 34 and x + 9y = −14 →
  14. 14.x + y = 1 and 2x − 4y = 20 →
  15. 15.7x + 6y = −5 and 6x + 7y = −21 →
  16. 16.5x + 5y = 25 and x − 6y = −37 →
  17. 17.x + 6y = 56 and 5x + y = 19 →
  18. 18.3x + y = 6 and x + 3y = 26 →
  19. 19.x − 3y = −23 and 6x + 6y = −18 →
  20. 20.2x + 6y = −34 and 3x − 4y = 1 →
  21. 21.5x + 3y = −15 and x + 4y = 14 →
  22. 22.5x + 4y = 14 and 4x + 5y = 22 →
  23. 23.6x + 6y = −78 and 5x − 4y = −11 →
  24. 24.3x + 5y = 7 and x + y = 1 →
  25. 25.5x − 5y = 50 and x + 6y = −46 →
  26. 26.6x + y = −11 and 6x + 4y = −26 →
  27. 27.9x + 5y = −2 and 5x + 9y = −26 →
  28. 28.8x + 2y = −62 and 2x + 8y = −68 →
  29. 29.6x + 5y = 65 and 2x + 4y = 38 →
  30. 30.7x + 6y = 117 and 6x + 7y = 117 →
  31. 31.x + 3y = 10 and 3x + y = 14 →
  32. 32.3x + y = 17 and 4x + 2y = 22 →
  33. 33.7x + 8y = 113 and 8x + 7y = 112 →
  34. 34.9x + y = 65 and x + 9y = 25 →
  35. 35.x + 6y = 21 and x − y = 0 →
  36. 36.x + 6y = −28 and 4x − 3y = −4 →
  37. 37.5x + 2y = 50 and 2x + 5y = 41 →
  38. 38.6x − 5y = 25 and 2x − y = 9 →
  39. 39.5x − y = 22 and 2x − 2y = 20 →
  40. 40.2x + 3y = 4 and 2x − 2y = 14 →

Answer key

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

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