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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 689 · 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. 1.3x + 2y = −10 and 2x + 5y = 19 →
  2. 2.3x − 5y = 2 and 5x − 6y = 15 →
  3. 3.4x + 5y = −18 and 5x + 4y = −9 →
  4. 4.6x + 3y = −36 and 3x + 6y = −54 →
  5. 5.4x + 6y = 6 and 6x + 4y = 24 →
  6. 6.6x − 5y = −1 and 4x + 2y = 26 →
  7. 7.x + 5y = −53 and 5x + y = −49 →
  8. 8.9x + y = −33 and x + 9y = −57 →
  9. 9.3x + 8y = −5 and 8x + 3y = 5 →
  10. 10.x + 3y = −7 and 6x − y = 15 →
  11. 11.5x + y = 31 and x + 5y = −37 →
  12. 12.x + y = −15 and 5x − 6y = −9 →
  13. 13.4x − 5y = 33 and x − 3y = 17 →
  14. 14.3x − 5y = −13 and 3x − 4y = −11 →
  15. 15.x + 6y = −27 and 6x + y = 13 →
  16. 16.2x + 2y = −34 and x + 5y = −53 →
  17. 17.3x + y = −20 and x + 4y = 19 →
  18. 18.8x + 2y = 4 and 2x + 8y = 46 →
  19. 19.3x + 3y = 33 and 2x + 3y = 25 →
  20. 20.5x − 2y = 11 and 3x + 2y = 13 →
  21. 21.5x − y = 0 and 5x + 6y = 35 →
  22. 22.x − 5y = 42 and x + 3y = −30 →
  23. 23.5x + 5y = −5 and 6x + 4y = −18 →
  24. 24.4x + 2y = −14 and 2x + 4y = 2 →
  25. 25.8x + 4y = 68 and 4x + 8y = 76 →
  26. 26.4x + y = −29 and x + 4y = −26 →
  27. 27.2x − y = 18 and 5x − 2y = 43 →
  28. 28.6x + 5y = −22 and 3x + 4y = −23 →
  29. 29.4x + 3y = −15 and 3x + 4y = −6 →
  30. 30.2x − 5y = 18 and x + y = −12 →
  31. 31.5x − 2y = 22 and x − 5y = −14 →
  32. 32.3x + y = 31 and x + 3y = 29 →
  33. 33.x + 2y = −4 and 2x + y = −14 →
  34. 34.2x + y = 2 and 6x − 5y = −42 →
  35. 35.5x + y = 1 and 4x − 3y = 35 →
  36. 36.x + 6y = −8 and 6x + 4y = −16 →
  37. 37.3x + 8y = 57 and 8x + 3y = 42 →
  38. 38.3x + 6y = −15 and 2x + y = 11 →
  39. 39.2x − y = 5 and 2x + y = 11 →
  40. 40.2x + 3y = −21 and 3x − 2y = 27 →

Answer key

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

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