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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 370 · 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 + 3y = 3 and 5x − 5y = 20 →
  2. 2.4x + 8y = −60 and 8x + 4y = −24 →
  3. 3.6x − 3y = 54 and 2x + 6y = −38 →
  4. 4.5x + y = 16 and 4x − y = 2 →
  5. 5.x − 5y = 28 and 5x − 6y = 64 →
  6. 6.x + 2y = 0 and 2x + y = −12 →
  7. 7.3x + 4y = 28 and 4x + y = 20 →
  8. 8.x + 8y = 13 and 8x + y = 41 →
  9. 9.9x + 2y = 61 and 2x + 9y = 5 →
  10. 10.6x + 7y = 9 and 7x + 6y = 17 →
  11. 11.5x + 2y = 31 and 3x + 2y = 13 →
  12. 12.3x + 2y = −2 and 4x − 5y = 51 →
  13. 13.9x + 8y = 48 and 8x + 9y = 37 →
  14. 14.4x + 6y = 34 and 6x + y = 43 →
  15. 15.6x − y = 21 and 6x − 5y = 9 →
  16. 16.x + 5y = 32 and 2x + 5y = 39 →
  17. 17.3x + 5y = 1 and 5x + 3y = 7 →
  18. 18.3x − 2y = −32 and 6x − 5y = −68 →
  19. 19.3x + y = 4 and x + 3y = 4 →
  20. 20.x − y = −14 and 3x + 6y = 3 →
  21. 21.x − 2y = −6 and 2x + 6y = −2 →
  22. 22.6x + 2y = 12 and 4x − 3y = 21 →
  23. 23.3x − 2y = −27 and x + 2y = −1 →
  24. 24.2x + y = −4 and 5x + y = −16 →
  25. 25.5x + 7y = 29 and 7x + 5y = 31 →
  26. 26.3x − 2y = 4 and 5x + 4y = 36 →
  27. 27.5x − 4y = 2 and 2x + 5y = 14 →
  28. 28.x + y = 0 and 4x + 5y = −1 →
  29. 29.2x + y = 13 and 4x − 4y = 8 →
  30. 30.5x + y = 32 and x + 5y = 16 →
  31. 31.6x + 2y = −52 and 4x + 3y = −43 →
  32. 32.3x + 8y = 79 and 8x + 3y = 64 →
  33. 33.6x + 5y = 41 and 6x − 3y = −15 →
  34. 34.6x + y = 13 and x + 6y = 8 →
  35. 35.4x − y = −17 and 5x + 2y = −31 →
  36. 36.8x + 2y = 62 and 2x + 8y = 38 →
  37. 37.3x − 3y = −3 and 5x − 4y = −3 →
  38. 38.2x − y = −18 and 3x + 3y = −18 →
  39. 39.5x + 8y = 77 and 8x + 5y = 53 →
  40. 40.x + 4y = 31 and 3x + 5y = 44 →

Answer key

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

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