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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 426 · 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. 1.7x + 9y = 87 and 9x + 7y = 89 →
  2. 2.x + 2y = −14 and 2x + y = −4 →
  3. 3.9x + 3y = 102 and 3x + 9y = 90 →
  4. 4.7x + 8y = 22 and 8x + 7y = 23 →
  5. 5.3x + 4y = 37 and x + 4y = 23 →
  6. 6.5x − 4y = −22 and x + 3y = 26 →
  7. 7.4x − 2y = −36 and 6x + 2y = −24 →
  8. 8.x + 3y = −3 and 5x + y = 27 →
  9. 9.x + 3y = 14 and 4x + 3y = 29 →
  10. 10.x − 2y = −6 and 5x + 2y = −6 →
  11. 11.4x + 4y = 52 and 6x − 2y = 6 →
  12. 12.6x + 9y = 21 and 9x + 6y = −21 →
  13. 13.2x + 6y = 54 and 3x + 5y = 57 →
  14. 14.6x + y = −58 and 4x + 2y = −44 →
  15. 15.2x + 6y = −14 and 6x + 2y = 22 →
  16. 16.x − 3y = −12 and 5x + y = −28 →
  17. 17.8x + y = −57 and x + 8y = 48 →
  18. 18.x − 6y = 27 and x + 4y = −33 →
  19. 19.9x + 4y = 59 and 4x + 9y = 84 →
  20. 20.x − 5y = 36 and 6x + 3y = −15 →
  21. 21.5x + 5y = 60 and 6x − 2y = 24 →
  22. 22.2x + 2y = −14 and x − 6y = 49 →
  23. 23.6x − 4y = 0 and x + 3y = 22 →
  24. 24.2x + y = −13 and x + 2y = −20 →
  25. 25.2x + 3y = 10 and 6x − 4y = 4 →
  26. 26.x + 3y = 31 and 2x + 3y = 35 →
  27. 27.x + 6y = −44 and x + y = −9 →
  28. 28.2x − 2y = 30 and x + 5y = −39 →
  29. 29.6x + 5y = 53 and 5x + 6y = 57 →
  30. 30.3x + 3y = 21 and 3x + y = 15 →
  31. 31.x − 3y = 6 and 5x + 3y = 48 →
  32. 32.6x + y = −52 and x − 5y = −19 →
  33. 33.6x + 8y = −20 and 8x + 6y = −8 →
  34. 34.6x + 8y = 52 and 8x + 6y = 32 →
  35. 35.7x + 3y = 33 and 3x + 7y = 37 →
  36. 36.3x + 8y = 49 and 8x + 3y = 39 →
  37. 37.6x + 3y = 0 and 4x + 5y = 6 →
  38. 38.x + 5y = 31 and 5x + y = 35 →
  39. 39.9x + 6y = 24 and 6x + 9y = 51 →
  40. 40.4x + 9y = −59 and 9x + 4y = −19 →

Answer key

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

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