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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 938 · 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 − 5y = 10 and 3x + 4y = 20 →
  2. 2.2x + y = 15 and x − 6y = −12 →
  3. 3.6x + y = −23 and x + 6y = 37 →
  4. 4.x − 4y = −14 and 5x + 2y = −26 →
  5. 5.6x + 6y = 84 and 6x + 3y = 69 →
  6. 6.2x + 5y = −2 and 5x + 4y = −22 →
  7. 7.7x + 3y = 84 and 3x + 7y = 76 →
  8. 8.9x + 6y = −45 and 6x + 9y = −75 →
  9. 9.3x + 4y = 51 and 6x + 3y = 72 →
  10. 10.2x + 3y = 1 and 3x + 2y = 4 →
  11. 11.5x + y = 53 and 6x + 3y = 78 →
  12. 12.3x + 4y = −1 and 4x + y = −10 →
  13. 13.6x − 3y = 21 and 4x + 6y = 70 →
  14. 14.2x + 2y = −12 and 4x − 4y = 40 →
  15. 15.4x − 5y = −37 and x − 3y = −25 →
  16. 16.2x + 6y = −34 and 4x + 2y = −28 →
  17. 17.4x + y = 43 and x − 6y = −33 →
  18. 18.4x + 6y = 10 and 2x + 5y = 7 →
  19. 19.9x + 2y = −3 and 2x + 9y = −52 →
  20. 20.5x − 6y = 23 and 2x + 2y = −26 →
  21. 21.x − 2y = −3 and x + y = −9 →
  22. 22.7x + 5y = −25 and 5x + 7y = −11 →
  23. 23.2x + 3y = −11 and 3x + 2y = 1 →
  24. 24.x − 3y = 24 and 5x + 4y = −13 →
  25. 25.6x − 6y = 60 and 2x + 5y = −43 →
  26. 26.4x − 2y = 4 and 2x + 2y = −16 →
  27. 27.x + 2y = 4 and 5x + 6y = 0 →
  28. 28.5x + y = 7 and x + 5y = 11 →
  29. 29.6x + 2y = 46 and 2x + y = 18 →
  30. 30.2x + 5y = −17 and 5x + 2y = 31 →
  31. 31.3x + y = −8 and 4x − 5y = −36 →
  32. 32.6x + 5y = 1 and 4x − y = −21 →
  33. 33.9x + 5y = 22 and 5x + 9y = 62 →
  34. 34.2x + 5y = 55 and 3x − y = 6 →
  35. 35.2x + 2y = 12 and 3x − y = −2 →
  36. 36.6x + 3y = −12 and 2x + 5y = −28 →
  37. 37.8x + 9y = −109 and 9x + 8y = −112 →
  38. 38.3x + 3y = 36 and 2x − 4y = −30 →
  39. 39.x + 3y = 17 and 3x + y = 27 →
  40. 40.2x − 6y = −34 and 6x − 6y = −6 →

Answer key

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

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