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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 344 · 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. 1.2x + y = 2 and 2x + 2y = 6 →
  2. 2.2x + 3y = −23 and 6x − 2y = 8 →
  3. 3.5x + 8y = 85 and 8x + 5y = 97 →
  4. 4.4x + 3y = −11 and 6x + 3y = −27 →
  5. 5.2x + 3y = 18 and x + 4y = 14 →
  6. 6.x + 5y = −19 and 2x + 2y = 2 →
  7. 7.2x + y = 8 and 3x − 6y = −3 →
  8. 8.6x + 9y = −18 and 9x + 6y = −42 →
  9. 9.x + 4y = 1 and 2x + 3y = −8 →
  10. 10.3x − y = −18 and 5x − 6y = −17 →
  11. 11.5x + 6y = 5 and 5x + y = −20 →
  12. 12.4x − 4y = 4 and 2x − y = 9 →
  13. 13.6x + y = 25 and x − 4y = −25 →
  14. 14.x + 2y = 10 and 4x + 5y = 16 →
  15. 15.3x + 6y = −48 and 2x + 2y = −24 →
  16. 16.x + 8y = −40 and 8x + y = 58 →
  17. 17.6x + 2y = 22 and x + 3y = −15 →
  18. 18.3x + 5y = 11 and 5x + 3y = 13 →
  19. 19.2x + 4y = −18 and 2x + 5y = −21 →
  20. 20.x − 3y = 17 and 5x − 2y = 46 →
  21. 21.2x − 2y = 10 and 5x + 3y = −31 →
  22. 22.2x + 2y = 26 and x − 3y = −15 →
  23. 23.6x − 5y = −63 and 3x + 6y = 45 →
  24. 24.x + 6y = −46 and 6x + y = 4 →
  25. 25.6x + y = 22 and 2x − 4y = −10 →
  26. 26.7x + 4y = 30 and 4x + 7y = 36 →
  27. 27.6x + 2y = 14 and 2x + 6y = 26 →
  28. 28.3x − 2y = 23 and 4x + 2y = −2 →
  29. 29.3x + y = −10 and 5x − 2y = 9 →
  30. 30.3x + y = 13 and x − 6y = 36 →
  31. 31.x + y = 18 and 6x − 2y = 36 →
  32. 32.5x + y = −29 and x + 5y = 23 →
  33. 33.2x + 4y = 26 and 2x + 3y = 19 →
  34. 34.6x + 2y = 52 and 2x − 3y = 10 →
  35. 35.8x + 9y = 76 and 9x + 8y = 77 →
  36. 36.x − y = 7 and 5x − 2y = 29 →
  37. 37.3x + y = 2 and x + 5y = −18 →
  38. 38.x − 5y = 36 and 6x + y = 30 →
  39. 39.2x − 3y = 3 and 4x − y = −19 →
  40. 40.x − 5y = −23 and 6x + 2y = 22 →

Answer key

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

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