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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 596 · 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. 1.8x + 7y = 39 and 7x + 8y = 51 →
  2. 2.6x + 4y = 70 and 4x + 6y = 60 →
  3. 3.3x − 5y = 51 and 3x − 6y = 60 →
  4. 4.2x − 3y = 16 and 3x − 2y = 4 →
  5. 5.3x + 8y = 45 and 8x + 3y = 65 →
  6. 6.4x + 5y = −7 and 5x + 4y = −11 →
  7. 7.x + 2y = 17 and 4x + 6y = 56 →
  8. 8.6x + 8y = 104 and 8x + 6y = 106 →
  9. 9.x − 5y = −26 and 2x + 3y = 39 →
  10. 10.2x + 5y = 56 and 5x + 2y = 56 →
  11. 11.7x + 3y = 87 and 3x + 7y = 83 →
  12. 12.4x − 3y = 11 and 2x + y = −7 →
  13. 13.6x − 6y = 30 and x − 6y = 20 →
  14. 14.x + y = 11 and x + 5y = 23 →
  15. 15.x + 5y = −25 and 6x − 6y = 66 →
  16. 16.x − 3y = −27 and x − y = −15 →
  17. 17.3x + y = 12 and x − 6y = 42 →
  18. 18.3x + 8y = 83 and 8x + 3y = 93 →
  19. 19.2x + 6y = 58 and 6x + y = 38 →
  20. 20.6x − y = −28 and 5x + 3y = −54 →
  21. 21.5x + 6y = 83 and x + y = 15 →
  22. 22.x + 2y = −3 and 4x + 6y = −4 →
  23. 23.2x − 5y = 63 and 3x − 2y = 45 →
  24. 24.2x + 5y = 51 and x + 6y = 57 →
  25. 25.4x + 2y = 26 and 2x + 4y = 22 →
  26. 26.4x + 2y = 0 and 4x − 2y = −8 →
  27. 27.7x + 4y = −28 and 4x + 7y = 17 →
  28. 28.6x + 2y = 14 and x + y = 3 →
  29. 29.3x + 3y = 0 and x + 4y = 6 →
  30. 30.3x − 2y = 1 and 2x + y = 3 →
  31. 31.4x + y = 30 and 4x + 3y = 42 →
  32. 32.x − 3y = −12 and 4x − 6y = −36 →
  33. 33.x + 2y = −10 and 3x + y = 0 →
  34. 34.3x − 4y = 32 and 2x − 5y = 33 →
  35. 35.2x + 6y = 34 and 3x + 2y = 23 →
  36. 36.5x + y = −17 and 6x + 3y = −6 →
  37. 37.4x + 2y = 50 and 4x − 3y = 15 →
  38. 38.x + 2y = 11 and x − 6y = −5 →
  39. 39.7x + y = −30 and x + 7y = −18 →
  40. 40.2x + 5y = −26 and 3x − 3y = 3 →

Answer key

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

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