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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 369 · 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. 1.6x + 8y = −80 and 8x + 6y = −88 →
  2. 2.6x − 5y = 93 and x + 3y = −19 →
  3. 3.5x + y = 34 and x − 3y = −6 →
  4. 4.6x + 7y = 33 and 7x + 6y = 19 →
  5. 5.5x − 4y = 2 and x − 2y = −2 →
  6. 6.4x + 6y = 66 and x − 4y = −33 →
  7. 7.4x + 9y = −47 and 9x + 4y = −57 →
  8. 8.6x − 3y = 12 and 6x − 5y = 4 →
  9. 9.x + 2y = 17 and 6x − 4y = −10 →
  10. 10.4x + 4y = −32 and 2x + 6y = −12 →
  11. 11.3x + 3y = −6 and 4x + 3y = −4 →
  12. 12.5x + 8y = −58 and 8x + 5y = −46 →
  13. 13.4x + 2y = −4 and 2x + 4y = −26 →
  14. 14.x + 3y = 5 and 6x + 6y = 6 →
  15. 15.x + 6y = 61 and 6x + 5y = 87 →
  16. 16.4x − 6y = 66 and 4x + 5y = 11 →
  17. 17.x + 9y = −37 and 9x + y = 67 →
  18. 18.3x + 3y = 6 and 5x + 2y = 7 →
  19. 19.4x + 8y = 36 and 8x + 4y = 0 →
  20. 20.9x + 3y = 72 and 3x + 9y = 96 →
  21. 21.5x + 2y = 25 and x − y = −2 →
  22. 22.4x + 3y = −19 and 2x + 4y = −32 →
  23. 23.6x + 3y = 21 and 6x − 2y = 16 →
  24. 24.2x + 7y = 25 and 7x + 2y = −25 →
  25. 25.2x + 7y = −11 and 7x + 2y = 29 →
  26. 26.2x + 3y = 31 and 3x + 3y = 39 →
  27. 27.4x + y = −35 and 4x + 4y = −44 →
  28. 28.4x + 2y = 50 and x + 4y = 37 →
  29. 29.6x + 3y = −54 and 6x − 2y = −34 →
  30. 30.4x + 4y = −16 and 5x + 6y = −15 →
  31. 31.7x + y = −55 and x + 7y = 47 →
  32. 32.7x + 8y = −6 and 8x + 7y = 6 →
  33. 33.x + 3y = 27 and 3x + y = 17 →
  34. 34.7x + 4y = 37 and 4x + 7y = 40 →
  35. 35.x + 8y = 57 and 8x + y = −48 →
  36. 36.5x − 4y = −18 and 5x + y = −8 →
  37. 37.x − 4y = −2 and 5x + 4y = 38 →
  38. 38.5x + 5y = 55 and 4x − 2y = 32 →
  39. 39.6x − 4y = 46 and x + 4y = 17 →
  40. 40.6x + 3y = 63 and 4x + 3y = 51 →

Answer key

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

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