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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 626 · 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. 1.5x + 3y = −12 and 3x + 5y = 12 →
  2. 2.7x + 5y = −2 and 5x + 7y = 2 →
  3. 3.3x + 3y = −21 and 5x + 4y = −26 →
  4. 4.6x + 4y = 66 and 4x + 6y = 64 →
  5. 5.4x + 5y = −13 and 5x + 4y = −23 →
  6. 6.6x − 4y = 30 and 3x + y = 33 →
  7. 7.6x − 6y = 12 and 3x + 5y = −2 →
  8. 8.2x − 5y = 37 and 4x − 2y = 34 →
  9. 9.4x + 7y = 35 and 7x + 4y = 53 →
  10. 10.4x + 6y = 58 and x − 3y = −17 →
  11. 11.4x − 6y = 44 and 5x − 2y = 33 →
  12. 12.9x + y = 57 and x + 9y = −47 →
  13. 13.6x + y = 39 and 5x − 3y = 67 →
  14. 14.4x − 3y = 27 and 6x + y = 13 →
  15. 15.2x − y = −21 and x + y = −3 →
  16. 16.5x + 6y = 17 and 3x + 3y = 9 →
  17. 17.5x + 9y = −32 and 9x + 5y = 32 →
  18. 18.6x − 4y = 20 and 5x − 2y = 6 →
  19. 19.6x − y = 13 and 4x + 5y = 37 →
  20. 20.8x + y = −30 and x + 8y = −51 →
  21. 21.6x − 5y = −4 and 5x − y = 22 →
  22. 22.5x + 5y = −20 and 5x + 2y = −5 →
  23. 23.5x + 2y = 53 and x + 2y = 17 →
  24. 24.x + 5y = −47 and 3x − 5y = 19 →
  25. 25.2x + 6y = 22 and 6x + 2y = 50 →
  26. 26.9x + 8y = 78 and 8x + 9y = 75 →
  27. 27.9x + y = 25 and x + 9y = 65 →
  28. 28.4x + 6y = −86 and 6x + 6y = −102 →
  29. 29.x − 2y = 3 and 2x − 3y = 4 →
  30. 30.x + 3y = 18 and 3x + y = −10 →
  31. 31.6x + 9y = 84 and 9x + 6y = 96 →
  32. 32.2x + 7y = 70 and 7x + 2y = 65 →
  33. 33.3x + 4y = −32 and 5x + 6y = −52 →
  34. 34.4x + 7y = 7 and 7x + 4y = −29 →
  35. 35.x − 6y = 51 and 2x + y = 11 →
  36. 36.6x + y = −27 and 3x + 5y = 27 →
  37. 37.3x + y = 10 and 3x + 5y = 14 →
  38. 38.2x − 5y = 41 and 4x − 3y = 47 →
  39. 39.5x − y = 31 and 5x + 2y = 58 →
  40. 40.4x + 2y = 14 and 4x + 5y = 17 →

Answer key

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

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