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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 542 · 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. 1.6x − 5y = −28 and x + y = 10 →
  2. 2.6x − 6y = 12 and 2x + 3y = 9 →
  3. 3.3x − y = −30 and 6x + 5y = −18 →
  4. 4.6x − 5y = −3 and x − 6y = −16 →
  5. 5.2x − 5y = −51 and 2x − 2y = −24 →
  6. 6.2x + 6y = 42 and x + 5y = 31 →
  7. 7.4x + 2y = 20 and 3x + 5y = 43 →
  8. 8.2x + 4y = 6 and 5x − 5y = 30 →
  9. 9.5x − 5y = −50 and 5x − 6y = −55 →
  10. 10.4x + 3y = −29 and x + 6y = −2 →
  11. 11.5x − 2y = 21 and 2x − 5y = 0 →
  12. 12.x + y = −5 and x − y = −9 →
  13. 13.6x + y = −11 and 6x + 3y = −21 →
  14. 14.2x + 5y = −21 and 3x − 5y = 56 →
  15. 15.6x + y = −8 and 3x + 6y = −15 →
  16. 16.6x + 5y = −29 and 5x + 6y = −37 →
  17. 17.5x + 6y = −18 and 6x + 5y = −26 →
  18. 18.5x + 2y = 16 and 2x + 5y = 19 →
  19. 19.x + 4y = −29 and 3x + 2y = −37 →
  20. 20.9x + y = 43 and x + 9y = −13 →
  21. 21.3x + 4y = 24 and x + 3y = 13 →
  22. 22.x − 4y = 31 and 2x + 6y = −50 →
  23. 23.4x + 7y = −11 and 7x + 4y = 22 →
  24. 24.5x + 6y = 11 and 6x + 5y = 11 →
  25. 25.9x + 8y = −31 and 8x + 9y = −20 →
  26. 26.6x + 3y = −33 and 3x + 6y = −30 →
  27. 27.6x + 3y = −27 and 3x + 6y = 18 →
  28. 28.x + 6y = 30 and 3x − 5y = −48 →
  29. 29.2x − 2y = 8 and 3x + 6y = 39 →
  30. 30.x + 4y = 14 and 2x − y = −17 →
  31. 31.6x − 5y = −3 and 2x − 5y = −11 →
  32. 32.6x + 2y = 16 and 2x + 3y = −11 →
  33. 33.x + 3y = 13 and 6x − 3y = 15 →
  34. 34.2x + y = −3 and x − 3y = 23 →
  35. 35.2x − 5y = −4 and 2x + 5y = 16 →
  36. 36.2x + 4y = 28 and 4x + 2y = 32 →
  37. 37.x − 5y = −43 and 3x − y = −3 →
  38. 38.3x − 4y = −46 and 5x + 2y = −16 →
  39. 39.x + 4y = −22 and 3x + 2y = −6 →
  40. 40.4x + 4y = −16 and x + 4y = 8 →

Answer key

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

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