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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 146 · 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 = −24 and 2x + 3y = −32 →
  2. 2.9x + 8y = −35 and 8x + 9y = −33 →
  3. 3.4x + 3y = 2 and 3x + 4y = 5 →
  4. 4.8x + 2y = 50 and 2x + 8y = 20 →
  5. 5.4x − 2y = 26 and 2x + 3y = −15 →
  6. 6.5x − y = 4 and 5x + y = 6 →
  7. 7.5x + 2y = 21 and 2x + 5y = 42 →
  8. 8.2x − 4y = −26 and 2x − 2y = −16 →
  9. 9.2x + 6y = −28 and 2x + 2y = −12 →
  10. 10.x + 2y = 13 and 2x + y = 17 →
  11. 11.6x − 6y = 6 and 5x + y = 41 →
  12. 12.3x − 3y = 9 and 3x + y = 17 →
  13. 13.5x + y = −6 and 3x + 4y = 27 →
  14. 14.5x + 5y = 15 and 4x − 5y = 3 →
  15. 15.4x + 6y = 66 and 3x − y = 11 →
  16. 16.2x + y = 15 and x + 2y = 12 →
  17. 17.4x + 6y = 24 and 2x − y = −12 →
  18. 18.x − 3y = −18 and 5x + 6y = 78 →
  19. 19.3x − 5y = 1 and 2x − 2y = −6 →
  20. 20.3x + y = −25 and x + 3y = −11 →
  21. 21.x + 3y = −7 and 3x − 4y = −8 →
  22. 22.9x + 6y = −117 and 6x + 9y = −108 →
  23. 23.4x − y = 21 and 4x + y = 3 →
  24. 24.x + 5y = 24 and 5x + y = 48 →
  25. 25.5x + 2y = −39 and x + y = −12 →
  26. 26.5x + 3y = −32 and 5x − 4y = −39 →
  27. 27.3x − 4y = −39 and 3x + 6y = 21 →
  28. 28.3x + 3y = 0 and 6x + 2y = −8 →
  29. 29.3x − 6y = 9 and 2x + y = 16 →
  30. 30.2x + 3y = −23 and 3x + 2y = −12 →
  31. 31.x + 5y = 35 and 5x + y = −17 →
  32. 32.x + 6y = −5 and 3x + 2y = 1 →
  33. 33.6x + y = 52 and 3x − y = 29 →
  34. 34.4x + 5y = −18 and 5x + 5y = −15 →
  35. 35.5x + 4y = 48 and 2x + 3y = 22 →
  36. 36.x + 5y = 1 and x − 2y = 8 →
  37. 37.2x + 3y = −11 and x + 6y = −1 →
  38. 38.2x + 3y = 37 and 3x + 2y = 38 →
  39. 39.4x + 4y = 4 and 5x + 2y = 8 →
  40. 40.6x + y = 19 and x + 6y = 44 →

Answer key

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

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