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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 592 · 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 − 5y = 32 and 3x + 3y = −36 →
  2. 2.4x + 6y = 66 and 6x + 4y = 74 →
  3. 3.3x + 7y = 13 and 7x + 3y = 57 →
  4. 4.4x + 3y = 28 and 3x + 4y = 35 →
  5. 5.8x + 3y = −10 and 3x + 8y = 10 →
  6. 6.4x + 3y = 31 and 2x + y = 15 →
  7. 7.x + y = −7 and 6x + 3y = −18 →
  8. 8.9x + 6y = −18 and 6x + 9y = 3 →
  9. 9.3x + 4y = −3 and x + 2y = 3 →
  10. 10.4x + 2y = −30 and 2x + 4y = −42 →
  11. 11.4x + y = 6 and x + 4y = −6 →
  12. 12.x + 2y = 21 and 2x + y = 15 →
  13. 13.5x + 6y = 77 and 6x + 5y = 77 →
  14. 14.3x − 4y = −17 and 5x + 5y = 30 →
  15. 15.7x + 8y = 44 and 8x + 7y = 46 →
  16. 16.2x + 6y = −36 and 6x + 2y = 4 →
  17. 17.2x − 2y = −24 and 4x + 2y = 0 →
  18. 18.9x + 6y = 63 and 6x + 9y = 72 →
  19. 19.2x + 3y = −7 and 2x + 6y = 2 →
  20. 20.4x + 3y = 5 and 2x − y = 15 →
  21. 21.4x + 2y = 20 and 5x − 6y = 42 →
  22. 22.3x − 5y = −12 and 4x + 6y = 22 →
  23. 23.3x + 9y = 57 and 9x + 3y = 27 →
  24. 24.3x + 5y = 29 and 2x + y = 10 →
  25. 25.5x − 3y = 18 and 2x − 2y = 4 →
  26. 26.x + 8y = 74 and 8x + y = 25 →
  27. 27.3x + y = 10 and x + 3y = −10 →
  28. 28.x + 5y = 36 and 4x − 5y = −56 →
  29. 29.6x + y = 27 and 6x + 6y = 72 →
  30. 30.2x + 5y = −36 and 6x + 4y = −64 →
  31. 31.3x − 6y = −33 and 4x − 4y = −16 →
  32. 32.4x + 8y = 28 and 8x + 4y = 20 →
  33. 33.7x + y = 34 and x + 7y = 46 →
  34. 34.4x − 4y = 8 and 6x + 3y = 3 →
  35. 35.5x + 7y = −2 and 7x + 5y = −22 →
  36. 36.2x − 2y = −2 and x − 6y = −36 →
  37. 37.8x + 3y = 16 and 3x + 8y = −49 →
  38. 38.3x + 7y = 7 and 7x + 3y = −37 →
  39. 39.5x − 4y = 3 and 2x − 3y = −10 →
  40. 40.4x + 4y = −32 and 5x + y = −12 →

Answer key

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

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