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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 680 · 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 − y = 13 and x + 3y = −13 →
  2. 2.5x − y = 23 and 3x + y = 25 →
  3. 3.6x + 2y = 56 and 2x + 5y = 23 →
  4. 4.6x + 5y = 53 and x − 2y = −11 →
  5. 5.x + 4y = −10 and 3x + 6y = −18 →
  6. 6.3x + 9y = 90 and 9x + 3y = 102 →
  7. 7.x + 2y = 10 and 2x + y = 8 →
  8. 8.4x + 5y = 29 and 5x + 4y = 25 →
  9. 9.3x + 2y = 26 and x + 4y = 12 →
  10. 10.6x + y = −19 and x + 6y = 26 →
  11. 11.x + 8y = −31 and 8x + y = 67 →
  12. 12.5x + 2y = 4 and 6x + 6y = −24 →
  13. 13.x + 3y = −4 and 2x − 5y = 36 →
  14. 14.5x + 5y = −35 and 3x + 4y = −29 →
  15. 15.x − 2y = 1 and 2x + 4y = −30 →
  16. 16.2x + 6y = 56 and 2x + 3y = 29 →
  17. 17.4x − 2y = −44 and 2x − 2y = −28 →
  18. 18.x + 3y = 10 and 3x + y = 6 →
  19. 19.4x + y = 45 and 4x − 6y = −18 →
  20. 20.x + 5y = 31 and 5x + y = 11 →
  21. 21.3x + y = 19 and x + 3y = 17 →
  22. 22.9x + 2y = 33 and 2x + 9y = 33 →
  23. 23.x + 9y = 39 and 9x + y = 31 →
  24. 24.x − y = 15 and x + 4y = −25 →
  25. 25.3x − 3y = −36 and 4x + 5y = −3 →
  26. 26.3x + 5y = 31 and 4x + y = 30 →
  27. 27.5x + y = −24 and x + 2y = −3 →
  28. 28.6x + y = 28 and x + 2y = 12 →
  29. 29.3x + 9y = 66 and 9x + 3y = 30 →
  30. 30.4x + y = 4 and x + 4y = −14 →
  31. 31.3x − 4y = −28 and 2x + 5y = −11 →
  32. 32.x + 3y = 32 and 3x + y = 32 →
  33. 33.3x − 5y = −21 and 3x − 3y = −9 →
  34. 34.6x + 2y = 44 and 2x − 2y = 28 →
  35. 35.5x − 3y = 46 and 5x + 2y = 11 →
  36. 36.2x + 8y = 34 and 8x + 2y = −44 →
  37. 37.6x + y = 9 and x + 6y = −51 →
  38. 38.x − 3y = −18 and 4x + y = 19 →
  39. 39.5x + 2y = −19 and 5x − 6y = −3 →
  40. 40.4x + 4y = 0 and x + 2y = −8 →

Answer key

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

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