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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 62 · 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 + y = 22 and x + 6y = 27 →
  2. 2.6x − 5y = 88 and x + 2y = −8 →
  3. 3.6x − 6y = 48 and 6x − 4y = 44 →
  4. 4.4x + y = 9 and 5x − 2y = 34 →
  5. 5.3x + 2y = −20 and 2x + 3y = −20 →
  6. 6.x − 4y = 5 and 4x + y = 3 →
  7. 7.6x + 5y = 18 and 4x + 6y = 28 →
  8. 8.4x + 3y = 3 and 3x + 4y = −3 →
  9. 9.2x + 3y = 17 and 5x + 3y = 29 →
  10. 10.2x + y = 4 and x + 2y = 5 →
  11. 11.x − 5y = −8 and 6x + 5y = 57 →
  12. 12.4x + 5y = −26 and 5x + 4y = −19 →
  13. 13.2x + 6y = −36 and 4x + 2y = 18 →
  14. 14.6x + y = −27 and x + 2y = −21 →
  15. 15.3x + y = −13 and 3x + 4y = 2 →
  16. 16.8x + 6y = −26 and 6x + 8y = −44 →
  17. 17.6x + y = −26 and x + 6y = 19 →
  18. 18.2x + y = 11 and x + 2y = 4 →
  19. 19.3x + 2y = 7 and x + y = 3 →
  20. 20.5x + 2y = 55 and 5x + 4y = 65 →
  21. 21.3x + 9y = 69 and 9x + 3y = −9 →
  22. 22.7x + y = −46 and x + 7y = 14 →
  23. 23.7x + 6y = 4 and 6x + 7y = −4 →
  24. 24.5x + 4y = −22 and x − 2y = −10 →
  25. 25.3x − 6y = −30 and x − 3y = −13 →
  26. 26.2x − 5y = −16 and x + y = 6 →
  27. 27.6x − 5y = 39 and 2x + 5y = −7 →
  28. 28.x + 8y = 23 and 8x + y = 58 →
  29. 29.3x + 3y = 39 and 3x − 6y = −24 →
  30. 30.5x + 3y = −37 and 4x − 3y = 19 →
  31. 31.2x − 6y = 46 and 6x + 3y = 33 →
  32. 32.8x + 3y = 8 and 3x + 8y = 58 →
  33. 33.x + 4y = 7 and 6x − y = −33 →
  34. 34.x + 4y = 5 and 3x − 5y = 32 →
  35. 35.3x + 4y = 23 and 3x − 2y = 11 →
  36. 36.6x + 3y = 36 and 3x + 6y = 36 →
  37. 37.3x + 5y = −13 and 5x − 6y = −36 →
  38. 38.3x + 3y = 18 and 2x + y = 7 →
  39. 39.3x + 6y = 57 and 5x + 2y = 23 →
  40. 40.5x − 5y = −40 and 6x + 6y = 60 →

Answer key

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

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