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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 346 · 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. 1.2x + 4y = 10 and 2x + 6y = 14 →
  2. 2.3x + 6y = −3 and 6x − y = 20 →
  3. 3.x + 3y = 12 and 2x + 3y = 3 →
  4. 4.5x − 6y = 56 and 6x − 3y = 42 →
  5. 5.5x − 4y = 41 and 4x + 6y = −50 →
  6. 6.x + 6y = −33 and x + 2y = −9 →
  7. 7.2x − 3y = −5 and x − 6y = −16 →
  8. 8.3x + 5y = 5 and 5x + 3y = −13 →
  9. 9.4x + 8y = 68 and 8x + 4y = 76 →
  10. 10.4x − y = 23 and 5x + 5y = 35 →
  11. 11.x + 6y = 52 and 2x − 6y = −40 →
  12. 12.2x − 3y = −36 and 5x + 4y = 2 →
  13. 13.4x + 4y = −16 and 2x − 5y = −15 →
  14. 14.x + 2y = −7 and 6x + 5y = −21 →
  15. 15.6x − 5y = 35 and 5x + y = 24 →
  16. 16.9x + 6y = −51 and 6x + 9y = −24 →
  17. 17.5x − y = 8 and 6x + y = 14 →
  18. 18.x − 2y = 17 and x + 6y = −31 →
  19. 19.x + 5y = 23 and 3x + y = 13 →
  20. 20.x + 2y = 12 and 6x + y = −27 →
  21. 21.6x + y = −54 and 5x − 4y = −16 →
  22. 22.2x + 2y = 2 and x − 2y = 16 →
  23. 23.4x − 2y = 20 and 3x + 5y = 41 →
  24. 24.4x + 5y = 1 and 5x + 5y = −5 →
  25. 25.6x + y = 35 and 4x + 6y = 50 →
  26. 26.4x + 6y = 2 and 6x + 4y = −22 →
  27. 27.3x + 2y = 25 and x + y = 11 →
  28. 28.8x + 2y = −32 and 2x + 8y = 52 →
  29. 29.7x + 9y = 33 and 9x + 7y = 15 →
  30. 30.8x + 3y = 79 and 3x + 8y = 64 →
  31. 31.3x − y = −11 and 2x − 3y = −12 →
  32. 32.x + 8y = −23 and 8x + y = 68 →
  33. 33.5x + 6y = −88 and 6x + 5y = −88 →
  34. 34.x − 6y = −18 and x + y = −4 →
  35. 35.6x + 7y = 20 and 7x + 6y = 19 →
  36. 36.2x + y = 2 and x + 2y = −5 →
  37. 37.6x + 5y = 27 and x + 3y = 24 →
  38. 38.5x + 2y = 34 and 2x + 5y = 1 →
  39. 39.x + 2y = 15 and 2x + y = 21 →
  40. 40.4x + 3y = 45 and 4x − 4y = 24 →

Answer key

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

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