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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 214 · 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 = −19 and 5x + y = 29 →
  2. 2.7x + 5y = −61 and 5x + 7y = −47 →
  3. 3.4x + y = 29 and 4x + 5y = 49 →
  4. 4.8x + 9y = 86 and 9x + 8y = 84 →
  5. 5.9x + 8y = 73 and 8x + 9y = 80 →
  6. 6.x + 7y = 68 and 7x + y = 44 →
  7. 7.x + 5y = 7 and x + 2y = 4 →
  8. 8.6x − 5y = 58 and 5x − 2y = 44 →
  9. 9.3x + 5y = 19 and 2x + y = 1 →
  10. 10.3x − y = 20 and 3x + 4y = 40 →
  11. 11.5x + 5y = 30 and 5x + 6y = 31 →
  12. 12.2x + 4y = 4 and 2x + 5y = 7 →
  13. 13.9x + 6y = 99 and 6x + 9y = 96 →
  14. 14.5x − 6y = 5 and 3x − 6y = 15 →
  15. 15.6x + 3y = 33 and 3x + 6y = 39 →
  16. 16.2x + 3y = 9 and 4x + 5y = 9 →
  17. 17.5x + 7y = 7 and 7x + 5y = −19 →
  18. 18.3x + 4y = 55 and 4x + 3y = 57 →
  19. 19.6x + 4y = −40 and 4x + 6y = −50 →
  20. 20.3x + 6y = 66 and 6x + 3y = 51 →
  21. 21.3x + 2y = −3 and 2x + 3y = 13 →
  22. 22.2x + 4y = −6 and 4x + 2y = 18 →
  23. 23.x + 4y = −33 and 6x + 5y = −27 →
  24. 24.8x + 7y = 127 and 7x + 8y = 128 →
  25. 25.7x + 2y = −18 and 2x + 7y = 27 →
  26. 26.3x + 5y = −26 and 3x + 3y = −12 →
  27. 27.x + 4y = 21 and 4x + y = 9 →
  28. 28.7x + 3y = −37 and 3x + 7y = −33 →
  29. 29.9x + 4y = −18 and 4x + 9y = 57 →
  30. 30.7x + 4y = −46 and 4x + 7y = −64 →
  31. 31.2x − 2y = −26 and 6x + 5y = 21 →
  32. 32.5x + 4y = 30 and 2x + 5y = 29 →
  33. 33.4x − 4y = 36 and x + 3y = 1 →
  34. 34.7x + 4y = 66 and 4x + 7y = 66 →
  35. 35.4x + 2y = 14 and 2x + 4y = 22 →
  36. 36.x + 4y = −30 and 4x + y = −15 →
  37. 37.6x + 9y = 60 and 9x + 6y = 45 →
  38. 38.x − 6y = −21 and 2x + 4y = −10 →
  39. 39.6x − 2y = 34 and 2x + 4y = −26 →
  40. 40.8x + 4y = −68 and 4x + 8y = −76 →

Answer key

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

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