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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 393 · 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. 1.6x + 3y = 36 and 3x − 5y = −34 →
  2. 2.4x + y = −6 and 6x + 4y = −14 →
  3. 3.7x + 4y = 72 and 4x + 7y = 60 →
  4. 4.x − 3y = 11 and 4x − 2y = 14 →
  5. 5.4x + 3y = 63 and x + y = 18 →
  6. 6.2x + 4y = 52 and 4x + 2y = 50 →
  7. 7.3x + 6y = 12 and 3x + 2y = −4 →
  8. 8.4x + 4y = 16 and 4x − 3y = −5 →
  9. 9.4x + 3y = 48 and 6x − 5y = −4 →
  10. 10.3x − 6y = −45 and 3x + 4y = −15 →
  11. 11.x + 6y = 55 and 5x + 3y = 32 →
  12. 12.2x + 4y = −12 and 3x − 4y = −28 →
  13. 13.x − 6y = 49 and 6x − y = −21 →
  14. 14.2x − 4y = 26 and x − 3y = 19 →
  15. 15.4x + y = 6 and x + 4y = 9 →
  16. 16.3x + 5y = −7 and 5x + 3y = −33 →
  17. 17.3x + y = 21 and 2x + 5y = 1 →
  18. 18.3x − 6y = 9 and 4x − y = 26 →
  19. 19.2x − 3y = −9 and 4x − 3y = 3 →
  20. 20.x + 3y = 11 and 5x − 4y = −2 →
  21. 21.5x + y = −9 and x + 5y = 27 →
  22. 22.6x − 3y = 21 and 4x − y = 17 →
  23. 23.6x + y = −20 and 3x + 5y = 8 →
  24. 24.5x + 3y = 31 and 3x + 5y = 25 →
  25. 25.3x + y = −7 and x + 3y = 3 →
  26. 26.6x + y = −4 and 4x − 2y = −8 →
  27. 27.2x + 4y = −32 and 4x + 2y = −10 →
  28. 28.8x + 3y = 46 and 3x + 8y = −24 →
  29. 29.x − 3y = −9 and 4x − 6y = −30 →
  30. 30.5x + 3y = 22 and 6x + 6y = 48 →
  31. 31.5x − 4y = 4 and 2x + y = 12 →
  32. 32.6x + 7y = −14 and 7x + 6y = 1 →
  33. 33.x − y = −5 and 5x + 3y = 39 →
  34. 34.x + 2y = −3 and x + 6y = −23 →
  35. 35.x + 3y = 25 and 6x − y = −2 →
  36. 36.5x + y = 18 and 4x − 3y = 3 →
  37. 37.4x − y = 26 and 3x + 3y = −3 →
  38. 38.5x + 8y = −117 and 8x + 5y = −117 →
  39. 39.4x + 8y = −96 and 8x + 4y = −84 →
  40. 40.8x + 7y = −44 and 7x + 8y = −31 →

Answer key

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

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