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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 180 · 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 + 6y = 72 and 6x − 4y = −18 →
  2. 2.6x − 6y = 6 and 6x + 4y = 76 →
  3. 3.2x + 3y = −21 and 3x + 2y = −19 →
  4. 4.4x − 5y = −16 and 3x + 2y = 11 →
  5. 5.5x − 4y = −56 and x − 5y = −28 →
  6. 6.3x − 5y = 4 and 2x + 3y = 28 →
  7. 7.5x − y = 18 and 6x + 5y = 34 →
  8. 8.5x + 2y = 19 and 6x − 5y = −29 →
  9. 9.5x + 6y = 20 and 2x + y = 1 →
  10. 10.x + 6y = 16 and 4x + 5y = 26 →
  11. 11.5x − 4y = 28 and x − 4y = 12 →
  12. 12.6x + y = −6 and 6x − 3y = −30 →
  13. 13.3x + 5y = 40 and 5x − y = 20 →
  14. 14.2x − 6y = −60 and 2x + 2y = 4 →
  15. 15.2x + 4y = 38 and 6x + 3y = 51 →
  16. 16.2x + y = 26 and 5x + 5y = 85 →
  17. 17.4x − 2y = 18 and x + 2y = 27 →
  18. 18.6x + 7y = −1 and 7x + 6y = 1 →
  19. 19.2x + 6y = 32 and 4x − 3y = 4 →
  20. 20.9x + 8y = −95 and 8x + 9y = −92 →
  21. 21.6x + y = −9 and x + 6y = 16 →
  22. 22.3x + 3y = 3 and x − 4y = 6 →
  23. 23.2x + 2y = 12 and 3x + 5y = 32 →
  24. 24.2x + 3y = −3 and 4x + y = −11 →
  25. 25.2x + 8y = 50 and 8x + 2y = 50 →
  26. 26.2x + 5y = −3 and 5x + 6y = −27 →
  27. 27.5x + 3y = 28 and x + 5y = −12 →
  28. 28.7x + y = 24 and x + 7y = 24 →
  29. 29.2x + 5y = −27 and 4x − 3y = 63 →
  30. 30.4x − 3y = 59 and 3x + y = 15 →
  31. 31.2x + 4y = −34 and 3x − 5y = 26 →
  32. 32.5x + 3y = 49 and 2x − 3y = −14 →
  33. 33.5x + 2y = 3 and 2x + 5y = −3 →
  34. 34.7x + 4y = −55 and 4x + 7y = −22 →
  35. 35.6x − 2y = −50 and 6x − 5y = −71 →
  36. 36.2x − 6y = −50 and 6x + 5y = 57 →
  37. 37.x − 5y = −35 and 4x + 6y = 68 →
  38. 38.4x + 2y = 14 and 5x + 4y = 31 →
  39. 39.6x + y = −17 and x + 6y = 38 →
  40. 40.x + 4y = −4 and 2x + 4y = −12 →

Answer key

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

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