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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 528 · 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 + 9y = 66 and 9x + 3y = 6 →
  2. 2.4x − 6y = −16 and 2x + 5y = 40 →
  3. 3.2x + y = −3 and x + 2y = −12 →
  4. 4.4x + 8y = 68 and 8x + 4y = 28 →
  5. 5.6x + 5y = 79 and 3x − 2y = 17 →
  6. 6.2x + y = 6 and 2x − y = −10 →
  7. 7.3x + 2y = −3 and 3x + 3y = −6 →
  8. 8.2x + 3y = 12 and 3x + 2y = 23 →
  9. 9.3x + 9y = 57 and 9x + 3y = −21 →
  10. 10.8x + 4y = −56 and 4x + 8y = −4 →
  11. 11.5x + 4y = 25 and x + 4y = 21 →
  12. 12.x + y = −6 and 6x − 2y = 36 →
  13. 13.2x + 5y = 53 and 5x + 2y = 38 →
  14. 14.2x + 5y = −55 and 2x + 6y = −64 →
  15. 15.2x + 6y = 38 and x + 4y = 24 →
  16. 16.2x + 4y = 34 and 6x + 5y = 60 →
  17. 17.2x + y = 20 and 6x − 2y = 20 →
  18. 18.9x + 2y = 56 and 2x + 9y = 21 →
  19. 19.9x + 8y = 3 and 8x + 9y = 14 →
  20. 20.2x + y = −4 and 4x + y = 0 →
  21. 21.x + y = 5 and 6x − 2y = 54 →
  22. 22.6x − 2y = −22 and 6x + 5y = 13 →
  23. 23.5x + 7y = −17 and 7x + 5y = −43 →
  24. 24.8x + 2y = −62 and 2x + 8y = 22 →
  25. 25.4x − y = 27 and 4x − 6y = 42 →
  26. 26.5x + 2y = −11 and 2x + 5y = 4 →
  27. 27.2x + 4y = −32 and 4x + 2y = −34 →
  28. 28.5x − 2y = 13 and 3x + 2y = 11 →
  29. 29.2x + 2y = 14 and 6x + 4y = 46 →
  30. 30.6x + 2y = −32 and 2x + 6y = 32 →
  31. 31.2x + 2y = 24 and 3x − 2y = 6 →
  32. 32.5x + 3y = 4 and 5x + y = −2 →
  33. 33.3x + 4y = 39 and 4x + 3y = 45 →
  34. 34.2x + y = 17 and 4x + y = 25 →
  35. 35.6x + 7y = 20 and 7x + 6y = 19 →
  36. 36.7x + 8y = −15 and 8x + 7y = 0 →
  37. 37.x + 4y = 29 and 4x − 2y = −28 →
  38. 38.9x + 4y = −85 and 4x + 9y = −45 →
  39. 39.2x + 6y = −38 and 4x + 6y = −34 →
  40. 40.6x + 2y = −64 and 6x − y = −49 →

Answer key

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

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