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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 546 · 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. 1.9x + 5y = 68 and 5x + 9y = 44 →
  2. 2.6x + 4y = −2 and 3x − 2y = −17 →
  3. 3.3x + y = 19 and x + 3y = 9 →
  4. 4.4x + 2y = 24 and 2x + 6y = 42 →
  5. 5.2x + 4y = 12 and 6x + 2y = 16 →
  6. 6.x − 4y = −11 and 5x − 6y = −27 →
  7. 7.3x + 5y = 10 and 4x − 3y = −35 →
  8. 8.x − 6y = −13 and x − y = 2 →
  9. 9.2x + 5y = 13 and 2x + 2y = −2 →
  10. 10.x + 8y = −68 and 8x + y = −40 →
  11. 11.6x + 8y = −52 and 8x + 6y = −46 →
  12. 12.5x + 3y = 13 and 3x + 5y = 11 →
  13. 13.5x + y = −3 and 5x + 4y = 18 →
  14. 14.4x + 2y = 12 and 6x + 6y = 24 →
  15. 15.3x + 2y = 27 and 2x + 3y = 28 →
  16. 16.2x + 2y = 14 and 4x + 2y = 20 →
  17. 17.x + 3y = −13 and x + 5y = −27 →
  18. 18.5x + y = 37 and x + 5y = −7 →
  19. 19.9x + 6y = −48 and 6x + 9y = −27 →
  20. 20.6x + 4y = 10 and 5x + 3y = 8 →
  21. 21.4x + y = 29 and 4x + 4y = 56 →
  22. 22.4x − 5y = 5 and 6x + y = 33 →
  23. 23.4x − 5y = 66 and 3x + 2y = 15 →
  24. 24.2x + 3y = −18 and x + 2y = −10 →
  25. 25.9x + 6y = −66 and 6x + 9y = −54 →
  26. 26.2x + 8y = 36 and 8x + 2y = 24 →
  27. 27.7x + 6y = 73 and 6x + 7y = 70 →
  28. 28.4x + 7y = −2 and 7x + 4y = −20 →
  29. 29.x + 2y = 6 and 6x − y = −29 →
  30. 30.x + 6y = 16 and 6x + y = 26 →
  31. 31.x + 9y = −29 and 9x + y = −21 →
  32. 32.4x − 3y = 41 and 5x + 2y = 34 →
  33. 33.3x + 4y = 19 and 6x + 4y = 46 →
  34. 34.2x + 2y = 26 and 3x + 2y = 31 →
  35. 35.2x + 8y = 66 and 8x + 2y = 84 →
  36. 36.8x + 2y = 22 and 2x + 8y = 28 →
  37. 37.9x + 5y = 117 and 5x + 9y = 121 →
  38. 38.5x + 4y = 42 and x + 5y = 21 →
  39. 39.7x + y = 70 and x + 7y = 58 →
  40. 40.x + 4y = 7 and 4x + y = −2 →

Answer key

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

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