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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 485 · 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.x + 2y = −6 and 3x − 3y = 45 →
  2. 2.9x + y = 35 and x + 9y = 75 →
  3. 3.5x + 7y = −8 and 7x + 5y = 8 →
  4. 4.x + 4y = 11 and 4x + y = 14 →
  5. 5.5x + 6y = 13 and 6x + 5y = 20 →
  6. 6.3x + 4y = 37 and x + y = 10 →
  7. 7.2x − 3y = 9 and 2x + 2y = 4 →
  8. 8.x + y = 12 and 2x + 6y = 40 →
  9. 9.6x − 2y = 44 and 4x + 4y = −8 →
  10. 10.7x + 2y = 39 and 2x + 7y = −21 →
  11. 11.7x + 8y = 85 and 8x + 7y = 80 →
  12. 12.4x + 6y = −6 and x + 2y = −3 →
  13. 13.4x + 5y = 77 and x + 2y = 26 →
  14. 14.4x + 3y = −2 and 6x + 2y = 2 →
  15. 15.x + 3y = 16 and x + y = 6 →
  16. 16.6x + 9y = 21 and 9x + 6y = 24 →
  17. 17.x + y = 9 and 4x − 2y = 18 →
  18. 18.5x − 6y = −57 and 4x + 5y = −26 →
  19. 19.8x + y = 47 and x + 8y = 61 →
  20. 20.x + 3y = 7 and 3x − 6y = 6 →
  21. 21.x + 3y = 2 and 3x − 5y = 34 →
  22. 22.9x + 8y = 34 and 8x + 9y = 34 →
  23. 23.3x + 4y = −42 and x + 5y = −36 →
  24. 24.6x + 5y = −79 and 3x + 2y = −37 →
  25. 25.5x − y = −46 and 2x + y = −10 →
  26. 26.6x + 9y = −12 and 9x + 6y = −3 →
  27. 27.2x + 8y = −62 and 8x + 2y = −38 →
  28. 28.2x + 5y = 47 and 5x + 3y = 51 →
  29. 29.5x − 4y = 43 and 4x + 5y = 18 →
  30. 30.4x − 2y = −4 and 4x + y = 14 →
  31. 31.2x + 6y = 4 and 5x + 2y = 23 →
  32. 32.5x − y = 33 and 2x − y = 15 →
  33. 33.x + 6y = 15 and x + y = 5 →
  34. 34.6x − 3y = 12 and 3x + y = 11 →
  35. 35.x + 2y = 10 and 2x + y = 14 →
  36. 36.3x + y = 15 and x + 3y = −3 →
  37. 37.2x + 3y = 15 and 2x + y = 9 →
  38. 38.5x + y = −49 and 4x − 4y = 4 →
  39. 39.3x − y = −23 and 6x + 5y = 10 →
  40. 40.5x + 9y = 36 and 9x + 5y = −36 →

Answer key

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

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