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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 535 · 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 + 4y = 10 and x + y = 4 →
  2. 2.4x − 2y = −48 and 6x + y = −40 →
  3. 3.x + 3y = −3 and 3x + y = 15 →
  4. 4.3x + 2y = 15 and 5x − 5y = −25 →
  5. 5.2x + 4y = −34 and x + y = −10 →
  6. 6.x + 5y = 28 and x + 2y = 13 →
  7. 7.5x + 4y = 39 and 3x + 5y = 26 →
  8. 8.2x + 3y = 12 and 3x + 2y = 13 →
  9. 9.6x + 4y = 36 and 4x + 6y = 44 →
  10. 10.8x + y = 50 and x + 8y = 22 →
  11. 11.3x + 2y = −1 and 5x + 4y = −3 →
  12. 12.6x + 2y = −44 and 2x + 6y = −4 →
  13. 13.9x + 2y = 23 and 2x + 9y = 65 →
  14. 14.4x + y = 14 and x + 4y = 26 →
  15. 15.3x − y = −19 and 5x + 2y = −28 →
  16. 16.5x + y = 37 and 4x + 3y = 45 →
  17. 17.4x + 6y = −2 and x + 5y = −4 →
  18. 18.6x + 4y = 36 and 4x − 4y = −16 →
  19. 19.6x + 5y = 70 and 5x + 6y = 73 →
  20. 20.6x + 7y = 9 and 7x + 6y = 4 →
  21. 21.5x + y = 17 and 2x − 2y = −10 →
  22. 22.7x + y = −4 and x + 7y = 20 →
  23. 23.4x + 3y = −29 and 2x − 5y = −21 →
  24. 24.x − 5y = −25 and 2x + 2y = 22 →
  25. 25.5x + 3y = −26 and 3x + 2y = −15 →
  26. 26.5x − 4y = 5 and x − 4y = −15 →
  27. 27.3x + 7y = 24 and 7x + 3y = 16 →
  28. 28.3x + 2y = 19 and 4x + 4y = 36 →
  29. 29.5x + 6y = −17 and 2x + y = −11 →
  30. 30.6x + y = 44 and x + 6y = 19 →
  31. 31.7x + 2y = −2 and 2x + 7y = −52 →
  32. 32.3x + 2y = 6 and 4x + 6y = 38 →
  33. 33.8x + 9y = 112 and 9x + 8y = 109 →
  34. 34.2x + 3y = 13 and 2x + 5y = 31 →
  35. 35.5x − 2y = 33 and 5x − 3y = 27 →
  36. 36.5x + 6y = −13 and 2x − 5y = 17 →
  37. 37.4x + y = −21 and 5x − 4y = 0 →
  38. 38.3x + 5y = 48 and 4x − y = −5 →
  39. 39.4x − 4y = −48 and 5x + 3y = −20 →
  40. 40.5x + y = 24 and x + 5y = 48 →

Answer key

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

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