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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 173 · 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 + 2y = −8 and 2x + 4y = −22 →
  2. 2.3x + y = 4 and 4x + 2y = 6 →
  3. 3.5x + y = 3 and x + 5y = −33 →
  4. 4.4x + 3y = 4 and 3x − 2y = 20 →
  5. 5.x − 2y = 2 and 5x + 5y = −20 →
  6. 6.x + 5y = 23 and 4x + 6y = 8 →
  7. 7.x + 6y = 34 and 4x + 2y = −18 →
  8. 8.3x − 5y = −17 and 6x − 3y = 15 →
  9. 9.5x + 5y = 50 and 2x + 3y = 21 →
  10. 10.x + 7y = 46 and 7x + y = 34 →
  11. 11.5x + 2y = −25 and 3x − 2y = −31 →
  12. 12.3x + 5y = −20 and 2x + 5y = −25 →
  13. 13.3x − 3y = −9 and 3x − y = −15 →
  14. 14.4x + 6y = −34 and 6x − y = 19 →
  15. 15.3x − 4y = 23 and 2x + 4y = −18 →
  16. 16.4x − 3y = −19 and 2x + y = 3 →
  17. 17.3x + 6y = 24 and 6x + 3y = −15 →
  18. 18.5x − 6y = −1 and 6x − 3y = 3 →
  19. 19.4x + 6y = 20 and 6x + 4y = 10 →
  20. 20.6x + 9y = 54 and 9x + 6y = 66 →
  21. 21.2x + 9y = 69 and 9x + 2y = 41 →
  22. 22.5x + 3y = −4 and x + 4y = −28 →
  23. 23.4x + 3y = −12 and 4x − 2y = −32 →
  24. 24.2x − 5y = 55 and 5x + 3y = −2 →
  25. 25.x − 6y = −21 and 4x + 2y = 46 →
  26. 26.3x + 8y = 66 and 8x + 3y = 66 →
  27. 27.2x + 8y = −26 and 8x + 2y = −74 →
  28. 28.4x + y = −2 and 5x + 3y = −13 →
  29. 29.5x − 2y = −20 and 5x + 6y = 20 →
  30. 30.6x − 2y = 16 and 5x + 2y = 17 →
  31. 31.3x + 2y = −33 and 2x − 5y = 16 →
  32. 32.5x + 6y = 4 and 5x − 4y = 14 →
  33. 33.5x − 4y = −34 and x − 5y = −11 →
  34. 34.5x − 2y = 27 and 2x − 6y = −10 →
  35. 35.2x + 2y = 26 and 2x + 6y = 54 →
  36. 36.2x + 7y = 38 and 7x + 2y = −2 →
  37. 37.x + 4y = −17 and 5x − 6y = 71 →
  38. 38.2x + 6y = 24 and 2x + 3y = 18 →
  39. 39.2x + 3y = 26 and x + y = 11 →
  40. 40.5x + 4y = 32 and 2x + y = 11 →

Answer key

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

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