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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 751 · 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.x + 7y = −11 and 7x + y = −29 →
  2. 2.x − 6y = −63 and 5x + 5y = 0 →
  3. 3.9x + 6y = 12 and 6x + 9y = −12 →
  4. 4.3x + 8y = 41 and 8x + 3y = −19 →
  5. 5.2x + 6y = 34 and 4x − 3y = −37 →
  6. 6.x − y = −1 and 2x + y = 4 →
  7. 7.3x + y = 18 and x + 2y = 21 →
  8. 8.2x − 4y = 28 and x − y = 8 →
  9. 9.3x − y = −4 and 6x + y = −5 →
  10. 10.6x + 8y = −58 and 8x + 6y = −40 →
  11. 11.x + 9y = 48 and 9x + y = 32 →
  12. 12.6x + 3y = 33 and 3x + 6y = 12 →
  13. 13.6x + 9y = −63 and 9x + 6y = −87 →
  14. 14.3x + 2y = 31 and 4x + 5y = 46 →
  15. 15.5x − 4y = −16 and 3x − 2y = −12 →
  16. 16.2x + 2y = 34 and 4x + 3y = 59 →
  17. 17.2x + 2y = 26 and 5x − 6y = −12 →
  18. 18.7x + y = 51 and x + 7y = 69 →
  19. 19.6x + 3y = −36 and 6x − 3y = −72 →
  20. 20.x + 3y = 13 and 3x + 4y = 24 →
  21. 21.6x + 2y = 44 and 4x + 2y = 32 →
  22. 22.3x + y = 0 and x + 3y = 24 →
  23. 23.7x + 6y = −50 and 6x + 7y = −54 →
  24. 24.6x + 5y = 34 and 5x + 6y = 21 →
  25. 25.4x + 2y = 24 and 5x + 2y = 29 →
  26. 26.4x + 6y = 4 and 6x + 4y = −4 →
  27. 27.5x + 4y = 65 and 2x + 2y = 28 →
  28. 28.9x + y = −62 and x + 9y = 2 →
  29. 29.5x + 4y = −19 and 5x − 3y = 23 →
  30. 30.3x + 5y = 64 and 6x + 2y = 64 →
  31. 31.5x + 8y = 32 and 8x + 5y = 59 →
  32. 32.6x + 3y = 9 and 6x − y = 5 →
  33. 33.x + 3y = 18 and 3x + y = −18 →
  34. 34.x + 2y = 3 and 2x + y = 9 →
  35. 35.5x + y = −20 and 5x − y = −30 →
  36. 36.6x + 5y = −6 and x − 6y = −42 →
  37. 37.2x + 2y = −32 and x − 6y = 40 →
  38. 38.x + 6y = 47 and 6x + y = 2 →
  39. 39.2x + 5y = −39 and 4x + y = −33 →
  40. 40.4x + 4y = −12 and 5x + 2y = −9 →

Answer key

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

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