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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 536 · 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. 1.4x + 3y = 2 and 3x + 4y = −2 →
  2. 2.x − 2y = 16 and x − 3y = 22 →
  3. 3.9x + 5y = −28 and 5x + 9y = −28 →
  4. 4.2x + 9y = 0 and 9x + 2y = 77 →
  5. 5.5x + 8y = −13 and 8x + 5y = −52 →
  6. 6.7x + 8y = 86 and 8x + 7y = 79 →
  7. 7.x + 2y = 3 and 3x + y = 4 →
  8. 8.4x + 2y = 8 and x + 4y = −5 →
  9. 9.4x − 6y = −18 and x + 5y = 54 →
  10. 10.2x + y = −12 and x + 2y = 0 →
  11. 11.3x + 5y = −62 and 6x + 4y = −82 →
  12. 12.4x − 4y = 52 and 4x + 4y = 12 →
  13. 13.x + 4y = 26 and 3x − y = 13 →
  14. 14.6x − 5y = −71 and x − 4y = −34 →
  15. 15.4x + 6y = 72 and x + 6y = 45 →
  16. 16.x + 9y = −74 and 9x + y = 54 →
  17. 17.x + 4y = 24 and 4x + y = −9 →
  18. 18.5x + 6y = 53 and 6x + 3y = 30 →
  19. 19.x + 2y = 1 and 3x − y = 31 →
  20. 20.6x − 4y = −10 and 4x + 2y = 26 →
  21. 21.x − 4y = 36 and 3x + 5y = −28 →
  22. 22.7x + y = 48 and x + 7y = −48 →
  23. 23.9x + 6y = −96 and 6x + 9y = −84 →
  24. 24.2x + 5y = 55 and x + 3y = 32 →
  25. 25.4x − 4y = 8 and 2x + 4y = −50 →
  26. 26.x + 5y = 3 and 6x + y = −11 →
  27. 27.2x − 2y = −4 and x + 6y = −23 →
  28. 28.x − 2y = 6 and 5x − y = 39 →
  29. 29.9x + 8y = −14 and 8x + 9y = −20 →
  30. 30.3x + 6y = −36 and 3x + 3y = −21 →
  31. 31.x + 3y = 18 and 3x + 4y = 14 →
  32. 32.5x + 3y = −19 and 3x + 5y = 11 →
  33. 33.5x + 6y = 15 and 3x + y = −4 →
  34. 34.4x + 3y = 26 and 3x + 4y = 30 →
  35. 35.2x − 6y = 22 and 3x + 2y = 22 →
  36. 36.6x + 2y = 72 and 4x − 5y = −9 →
  37. 37.4x + 6y = 32 and 5x + 3y = 22 →
  38. 38.2x + 6y = −8 and 2x + 3y = −5 →
  39. 39.x − 5y = −8 and 4x − 5y = −2 →
  40. 40.9x + 7y = 69 and 7x + 9y = 75 →

Answer key

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

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