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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 955 · 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 + 4y = 23 and 4x + 5y = 31 →
  2. 2.5x + 6y = −29 and 6x + 5y = −37 →
  3. 3.5x + 7y = 87 and 7x + 5y = 93 →
  4. 4.7x + 3y = 58 and 3x + 7y = 42 →
  5. 5.3x + 2y = −7 and 2x + 3y = 2 →
  6. 6.6x − 6y = −36 and 4x + 4y = 32 →
  7. 7.6x + 6y = 36 and 3x + 2y = 16 →
  8. 8.x + 3y = −10 and 2x + y = 5 →
  9. 9.4x + y = 25 and 6x + 6y = 78 →
  10. 10.7x + 2y = −46 and 2x + 7y = −71 →
  11. 11.8x + 3y = 27 and 3x + 8y = 17 →
  12. 12.6x + 2y = 38 and 5x + y = 27 →
  13. 13.8x + 3y = 77 and 3x + 8y = 77 →
  14. 14.3x + 9y = 30 and 9x + 3y = −6 →
  15. 15.5x + 2y = 23 and 4x + 2y = 18 →
  16. 16.2x + 6y = −34 and 6x + 5y = −37 →
  17. 17.4x − 5y = −17 and x − 3y = −13 →
  18. 18.x + 2y = 12 and 2x + y = 9 →
  19. 19.4x + 6y = −52 and 4x + 4y = −36 →
  20. 20.2x + 5y = 9 and 5x + 2y = 12 →
  21. 21.5x + 6y = −46 and 4x + 4y = −32 →
  22. 22.4x − 4y = 24 and 4x + 5y = 15 →
  23. 23.5x + 3y = 16 and x + 4y = 27 →
  24. 24.x + 6y = 55 and 6x + y = 50 →
  25. 25.2x − y = −11 and 5x + 4y = −73 →
  26. 26.6x + 3y = −42 and 2x − 5y = −38 →
  27. 27.2x + y = 19 and 4x + 3y = 41 →
  28. 28.3x + y = 21 and x + 3y = −9 →
  29. 29.5x + 6y = 74 and 6x + 5y = 69 →
  30. 30.2x + y = 14 and 6x + 4y = 44 →
  31. 31.9x + 7y = 90 and 7x + 9y = 102 →
  32. 32.4x − 2y = 24 and 3x − 4y = 28 →
  33. 33.4x + y = 15 and x + 4y = 30 →
  34. 34.2x + 5y = −12 and 5x + 2y = 12 →
  35. 35.6x + 3y = −27 and 4x + y = −17 →
  36. 36.5x + 2y = 49 and 4x + 4y = 56 →
  37. 37.3x − y = −29 and x + 5y = 17 →
  38. 38.3x + 5y = 48 and 5x + 3y = 32 →
  39. 39.6x − y = −6 and 5x + 4y = −34 →
  40. 40.x − 6y = 20 and 4x − 6y = 8 →

Answer key

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

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