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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 753 · 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 + 2y = 32 and 5x + 3y = 38 →
  2. 2.2x + y = 19 and x + 2y = 14 →
  3. 3.5x + 2y = 55 and 2x + 5y = 43 →
  4. 4.5x + 2y = 0 and 3x + 2y = 4 →
  5. 5.3x − 4y = −38 and 3x − 6y = −54 →
  6. 6.6x − 3y = 30 and 5x + 5y = 55 →
  7. 7.2x − 5y = 35 and 5x − 6y = 55 →
  8. 8.8x + 5y = −32 and 5x + 8y = −59 →
  9. 9.x − 3y = −22 and 5x − y = 2 →
  10. 10.7x + y = −6 and x + 7y = 54 →
  11. 11.8x + 3y = 25 and 3x + 8y = −25 →
  12. 12.3x + y = 2 and x + 3y = −18 →
  13. 13.6x + y = 47 and 2x − 5y = −11 →
  14. 14.5x + 2y = 35 and x + 4y = 25 →
  15. 15.5x + 5y = 45 and 5x − 4y = 0 →
  16. 16.3x − y = 2 and 2x − 6y = −36 →
  17. 17.x + 7y = −3 and 7x + y = 27 →
  18. 18.9x + y = 13 and x + 9y = 37 →
  19. 19.x + y = 10 and 2x + 6y = 48 →
  20. 20.4x − y = 37 and 3x + 5y = −1 →
  21. 21.7x + 8y = 29 and 8x + 7y = 31 →
  22. 22.5x + 2y = 35 and 2x + 5y = −7 →
  23. 23.3x + 4y = −22 and 2x − y = 11 →
  24. 24.3x + 4y = 38 and x + 6y = 50 →
  25. 25.3x + y = 5 and x + 3y = 7 →
  26. 26.2x + y = −15 and x + 2y = −15 →
  27. 27.3x + 4y = −7 and 2x + y = −13 →
  28. 28.5x + y = 41 and 3x + 4y = 45 →
  29. 29.8x + 4y = −28 and 4x + 8y = 40 →
  30. 30.4x + 3y = −15 and 2x − y = −25 →
  31. 31.2x − 2y = 4 and x − 4y = −10 →
  32. 32.5x + y = −14 and x + 5y = −22 →
  33. 33.6x + 7y = 15 and 7x + 6y = 24 →
  34. 34.5x + 3y = 11 and 4x − 4y = −4 →
  35. 35.4x + 3y = 1 and x + 5y = 13 →
  36. 36.2x + 4y = −46 and 4x + 2y = −44 →
  37. 37.6x − 5y = 1 and 3x + 6y = 9 →
  38. 38.2x + 8y = 4 and 8x + 2y = 46 →
  39. 39.x + 2y = 3 and 2x + y = 9 →
  40. 40.3x + 5y = 16 and x − y = 0 →

Answer key

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

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