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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 846 · 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. 1.2x + 2y = 28 and 3x + 2y = 37 →
  2. 2.7x + 6y = −20 and 6x + 7y = −32 →
  3. 3.7x + y = 30 and x + 7y = 18 →
  4. 4.6x + 2y = −8 and 2x + 6y = 8 →
  5. 5.x + y = 13 and 2x + y = 22 →
  6. 6.6x + 5y = −15 and 5x + 6y = −29 →
  7. 7.5x + 8y = 93 and 8x + 5y = 102 →
  8. 8.x + 7y = 15 and 7x + y = 9 →
  9. 9.x + 8y = 63 and 8x + y = −63 →
  10. 10.8x + 4y = 44 and 4x + 8y = 16 →
  11. 11.x + 3y = −8 and x + 5y = −12 →
  12. 12.5x − y = 36 and 4x − y = 30 →
  13. 13.x + 3y = 10 and 2x + y = 10 →
  14. 14.2x + 4y = 30 and 2x + 5y = 36 →
  15. 15.2x + 6y = 36 and 6x + 2y = 60 →
  16. 16.x + 5y = 28 and 5x + 5y = 40 →
  17. 17.6x + 7y = −5 and 7x + 6y = 5 →
  18. 18.x + y = 11 and 3x + 5y = 43 →
  19. 19.3x − 2y = −33 and 2x − 2y = −26 →
  20. 20.3x + y = 14 and x + 3y = 10 →
  21. 21.3x + y = 1 and x + 3y = −21 →
  22. 22.3x + 2y = −6 and 6x − 5y = 42 →
  23. 23.x + 3y = 1 and 3x + y = −13 →
  24. 24.8x + 3y = 82 and 3x + 8y = 72 →
  25. 25.x + 4y = −22 and 4x + 3y = −23 →
  26. 26.3x + 5y = 33 and 2x − 6y = −34 →
  27. 27.2x + 5y = −28 and x − 5y = 16 →
  28. 28.6x + y = 49 and x + 6y = 14 →
  29. 29.3x + 4y = 23 and 4x + 3y = 33 →
  30. 30.7x + 6y = −15 and 6x + 7y = −11 →
  31. 31.x + y = −6 and 5x + 4y = −26 →
  32. 32.6x + 2y = 6 and 2x − 6y = 22 →
  33. 33.2x + 7y = 61 and 7x + 2y = 11 →
  34. 34.9x + y = −28 and x + 9y = −12 →
  35. 35.6x + 6y = −60 and 5x + 4y = −46 →
  36. 36.6x + 6y = 30 and 6x + y = 15 →
  37. 37.3x + 4y = 15 and 4x + 3y = −1 →
  38. 38.x + 3y = −4 and 3x + y = −20 →
  39. 39.2x + 5y = 36 and 5x + 2y = 27 →
  40. 40.8x + 7y = 16 and 7x + 8y = 29 →

Answer key

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

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