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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 533 · 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 − 6y = 38 and x + 6y = −62 →
  2. 2.5x + 6y = −8 and x − 4y = 40 →
  3. 3.6x + 5y = 88 and 3x − 2y = 8 →
  4. 4.x + 4y = 13 and x + y = 4 →
  5. 5.6x + 6y = 36 and 4x + 6y = 18 →
  6. 6.x + 2y = 12 and 3x − 5y = −8 →
  7. 7.9x + 4y = −32 and 4x + 9y = −7 →
  8. 8.9x + y = 53 and x + 9y = 77 →
  9. 9.3x − 6y = 18 and 5x + y = 8 →
  10. 10.4x + 6y = −18 and x + 3y = −12 →
  11. 11.x + 2y = 16 and 6x + 2y = 46 →
  12. 12.3x − 3y = 12 and x + 2y = 13 →
  13. 13.8x + 7y = −36 and 7x + 8y = −39 →
  14. 14.x + 2y = −18 and 2x + y = −15 →
  15. 15.2x − 4y = 16 and 2x + 2y = 10 →
  16. 16.x − y = 16 and 3x − 6y = 69 →
  17. 17.2x + y = 3 and 4x − y = 3 →
  18. 18.9x + 6y = −9 and 6x + 9y = −36 →
  19. 19.5x − 6y = −23 and x + 2y = −11 →
  20. 20.5x − 6y = −40 and 2x + 2y = 6 →
  21. 21.6x + 6y = −18 and 6x + y = −28 →
  22. 22.x + 3y = −8 and 6x + 2y = 32 →
  23. 23.x − 6y = −14 and 2x + y = −2 →
  24. 24.3x + 5y = 3 and 5x − 6y = −81 →
  25. 25.3x − 6y = −27 and 3x + y = 8 →
  26. 26.4x − y = −29 and 2x − y = −19 →
  27. 27.4x + 4y = 16 and 3x − 6y = 48 →
  28. 28.2x + y = 11 and x + y = 6 →
  29. 29.x + 4y = 9 and 5x + 4y = 13 →
  30. 30.4x − 3y = −54 and 5x − y = −51 →
  31. 31.5x − y = −17 and 5x − 2y = −24 →
  32. 32.9x + 4y = 76 and 4x + 9y = 41 →
  33. 33.x + 9y = 30 and 9x + y = 30 →
  34. 34.2x + 5y = 48 and 5x + 2y = 57 →
  35. 35.6x + 2y = 56 and 2x + 6y = 24 →
  36. 36.x − y = −1 and 6x + 6y = 18 →
  37. 37.8x + 2y = 26 and 2x + 8y = 14 →
  38. 38.4x + 2y = −14 and 2x + 4y = −10 →
  39. 39.8x + 3y = 60 and 3x + 8y = 50 →
  40. 40.x − 6y = 49 and 3x − 4y = 49 →

Answer key

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

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