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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 400 · 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 − 3y = −23 and x + 3y = 31 →
  2. 2.2x + 4y = −22 and 4x + 2y = −8 →
  3. 3.x + 2y = 1 and 4x + y = −31 →
  4. 4.2x + 2y = 20 and x − 6y = −32 →
  5. 5.x + y = −3 and 4x + 3y = −17 →
  6. 6.2x − 5y = 7 and 2x + 2y = 14 →
  7. 7.x − y = 12 and x + 3y = −12 →
  8. 8.4x + 3y = −1 and 4x + 2y = −2 →
  9. 9.4x + y = 31 and x + y = 7 →
  10. 10.3x + 5y = −17 and 5x + 3y = 9 →
  11. 11.3x + 2y = 39 and 2x + 3y = 41 →
  12. 12.3x + 2y = −15 and 2x + 3y = 0 →
  13. 13.2x + 3y = −24 and 4x − y = −34 →
  14. 14.3x + 2y = 1 and 2x + 3y = 9 →
  15. 15.2x + 9y = 57 and 9x + 2y = 64 →
  16. 16.4x + 6y = −20 and 4x − 3y = −38 →
  17. 17.3x + 3y = −12 and 3x + 4y = −7 →
  18. 18.3x + 2y = 2 and 2x + 3y = 8 →
  19. 19.8x + 5y = 45 and 5x + 8y = 33 →
  20. 20.x + 2y = −3 and 5x + 6y = −11 →
  21. 21.6x + 2y = 52 and 2x + 6y = 12 →
  22. 22.x − y = 3 and 6x + 4y = 8 →
  23. 23.x + 5y = −46 and 5x + y = −38 →
  24. 24.5x + y = 28 and 3x − 4y = −20 →
  25. 25.2x + 3y = 15 and 2x − 4y = −48 →
  26. 26.x + 9y = 75 and 9x + y = −45 →
  27. 27.3x + 6y = 9 and 2x + y = −6 →
  28. 28.2x − 4y = −4 and x + 5y = 33 →
  29. 29.8x + 9y = 34 and 9x + 8y = 34 →
  30. 30.2x + 3y = −14 and 2x + 6y = −32 →
  31. 31.2x − 2y = 2 and x − 3y = 15 →
  32. 32.x + 3y = −17 and 2x − 4y = 46 →
  33. 33.3x + 9y = 0 and 9x + 3y = 24 →
  34. 34.5x − 4y = −13 and 2x + 2y = 20 →
  35. 35.4x + 5y = 20 and 5x − 4y = −57 →
  36. 36.7x + 9y = 144 and 9x + 7y = 144 →
  37. 37.3x + 6y = −33 and 5x − 4y = 1 →
  38. 38.9x + 6y = 18 and 6x + 9y = 57 →
  39. 39.2x − 2y = −6 and 5x + 6y = 84 →
  40. 40.2x + 9y = 35 and 9x + 2y = 42 →

Answer key

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

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