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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 887 · 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 + 5y = 6 and 3x + 6y = 0 →
  2. 2.3x + 5y = 27 and 3x + 6y = 30 →
  3. 3.2x − 6y = −42 and 2x − y = 3 →
  4. 4.x − 6y = −24 and 2x + 5y = 37 →
  5. 5.5x + 4y = −11 and 2x + 5y = 16 →
  6. 6.x + 8y = 48 and 8x + y = 69 →
  7. 7.5x + y = −40 and x + 5y = 16 →
  8. 8.3x − y = 8 and 2x − 4y = 12 →
  9. 9.3x + y = 12 and 2x + y = 10 →
  10. 10.4x − y = 4 and 2x − y = −2 →
  11. 11.6x − 5y = 3 and 5x − y = 12 →
  12. 12.x − 2y = −8 and x + 2y = 24 →
  13. 13.6x + 4y = 28 and 4x + 6y = 22 →
  14. 14.x + 2y = 11 and 2x + y = −2 →
  15. 15.4x + 3y = 47 and 3x + 4y = 44 →
  16. 16.4x + 8y = 80 and 8x + 4y = 52 →
  17. 17.2x − 5y = 9 and 4x − 3y = −3 →
  18. 18.x + 3y = −17 and 2x + 4y = −24 →
  19. 19.6x + 4y = 62 and 4x + 6y = 58 →
  20. 20.3x + 7y = 49 and 7x + 3y = 61 →
  21. 21.6x + 2y = 56 and 3x + 4y = 49 →
  22. 22.5x + 7y = 48 and 7x + 5y = 24 →
  23. 23.6x + y = −7 and 4x + 6y = −10 →
  24. 24.5x + 6y = 73 and x + 5y = 45 →
  25. 25.3x + 2y = 0 and x − 3y = −11 →
  26. 26.5x + 7y = 88 and 7x + 5y = 80 →
  27. 27.x + 4y = 13 and 4x − y = 18 →
  28. 28.4x + 2y = 36 and x + y = 13 →
  29. 29.5x + 3y = 30 and 6x − 6y = −12 →
  30. 30.x + 5y = 29 and 5x + y = −23 →
  31. 31.5x + 6y = −8 and 3x + 2y = 0 →
  32. 32.9x + 3y = 9 and 3x + 9y = 51 →
  33. 33.8x + 5y = 74 and 5x + 8y = 56 →
  34. 34.5x + 8y = 2 and 8x + 5y = −28 →
  35. 35.4x + 8y = 36 and 8x + 4y = 48 →
  36. 36.4x + 6y = −74 and 6x + 2y = −48 →
  37. 37.5x − y = 26 and x + 6y = −32 →
  38. 38.5x − 6y = 12 and x + 2y = −20 →
  39. 39.3x + 4y = 1 and 3x + y = 16 →
  40. 40.6x + y = 21 and x + 5y = −11 →

Answer key

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

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