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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 714 · 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. 1.7x + y = 44 and x + 7y = −28 →
  2. 2.7x + y = 25 and x + 7y = 31 →
  3. 3.6x + y = 26 and x + 6y = 51 →
  4. 4.3x + y = 20 and 2x + y = 14 →
  5. 5.3x − 5y = −14 and 4x − 6y = −16 →
  6. 6.3x + 6y = 6 and 6x + 6y = −12 →
  7. 7.6x + 7y = 33 and 7x + 6y = 32 →
  8. 8.2x + 2y = 22 and 2x + y = 16 →
  9. 9.4x + 5y = −13 and 5x + 6y = −15 →
  10. 10.6x + 3y = −39 and x − 2y = −9 →
  11. 11.5x − 5y = 40 and 2x − 5y = 31 →
  12. 12.2x + 7y = 21 and 7x + 2y = 51 →
  13. 13.7x + 2y = 53 and 2x + 7y = 28 →
  14. 14.4x + 3y = −4 and 3x + 4y = −17 →
  15. 15.5x − 2y = −2 and 4x − 2y = −4 →
  16. 16.4x + 3y = 6 and 4x + 5y = −6 →
  17. 17.4x − 4y = −24 and 2x − 6y = −24 →
  18. 18.3x + 9y = 63 and 9x + 3y = 45 →
  19. 19.5x + 6y = −58 and 5x − 5y = −25 →
  20. 20.x + 6y = 33 and 6x + 2y = −40 →
  21. 21.x + 5y = −44 and x + 4y = −35 →
  22. 22.9x + 8y = 39 and 8x + 9y = 46 →
  23. 23.4x − 5y = −21 and 2x + 5y = 57 →
  24. 24.3x + y = 26 and 6x + 5y = 76 →
  25. 25.4x + y = 4 and 6x + y = 8 →
  26. 26.5x + y = −12 and x + 5y = 36 →
  27. 27.9x + 3y = −93 and 3x + 9y = −87 →
  28. 28.5x + 3y = 34 and 2x + 2y = 16 →
  29. 29.2x + 8y = 32 and 8x + 2y = 68 →
  30. 30.6x + 4y = 44 and 4x + 6y = 36 →
  31. 31.x − 4y = 4 and 6x + 4y = 52 →
  32. 32.x − 4y = −33 and x − 6y = −51 →
  33. 33.x + 5y = −7 and 6x + 5y = 33 →
  34. 34.5x + 6y = 40 and 4x + 2y = 18 →
  35. 35.4x + 3y = 1 and 4x + 4y = 4 →
  36. 36.3x − 4y = −29 and 5x + 2y = 21 →
  37. 37.4x − 4y = −24 and 5x + 2y = 33 →
  38. 38.9x + y = 11 and x + 9y = −61 →
  39. 39.4x + 3y = 27 and x − y = 5 →
  40. 40.6x + 7y = 3 and 7x + 6y = −3 →

Answer key

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

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