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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 617 · 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. 1.9x + 2y = −62 and 2x + 9y = −48 →
  2. 2.2x + 3y = 34 and 3x + 2y = 31 →
  3. 3.2x − 6y = −48 and 5x + 4y = 51 →
  4. 4.4x − y = 32 and 5x + 6y = 69 →
  5. 5.4x + 5y = 34 and 5x + 4y = 29 →
  6. 6.5x − 6y = 58 and 6x − y = 20 →
  7. 7.7x + 6y = −18 and 6x + 7y = −8 →
  8. 8.5x + y = 35 and x + 5y = −17 →
  9. 9.x + 5y = 9 and 5x + y = 21 →
  10. 10.x + 8y = 0 and 8x + y = −63 →
  11. 11.2x − 6y = −52 and 3x − 2y = −22 →
  12. 12.4x − y = −37 and 5x + y = −44 →
  13. 13.6x + 4y = 48 and 5x − 2y = −8 →
  14. 14.x + 3y = 11 and 3x + y = 9 →
  15. 15.5x − 3y = 9 and 6x + 3y = 24 →
  16. 16.5x − 4y = −35 and x − 2y = −13 →
  17. 17.5x + 3y = −7 and 5x − y = 29 →
  18. 18.4x + 4y = 20 and x − 5y = −1 →
  19. 19.6x + 2y = −4 and 2x + 6y = 20 →
  20. 20.5x − 6y = 19 and 2x + 2y = 12 →
  21. 21.4x + 4y = 36 and 6x + 2y = 34 →
  22. 22.5x + 2y = 16 and 4x + 5y = 23 →
  23. 23.4x + 3y = 38 and 5x + 2y = 44 →
  24. 24.3x + 5y = 9 and 2x − 2y = −10 →
  25. 25.5x − 4y = −6 and 2x − 4y = −24 →
  26. 26.6x + 8y = 20 and 8x + 6y = 8 →
  27. 27.2x + 8y = 56 and 8x + 2y = 44 →
  28. 28.2x + 6y = 58 and x − y = −3 →
  29. 29.x − 2y = 7 and 6x + 5y = −43 →
  30. 30.x + 4y = 24 and 5x − 3y = 28 →
  31. 31.6x + y = 26 and x − 3y = −2 →
  32. 32.9x + 4y = −34 and 4x + 9y = 21 →
  33. 33.x + 6y = −50 and 6x + y = −20 →
  34. 34.3x + 2y = −10 and 5x + 6y = −6 →
  35. 35.6x − 6y = 36 and 6x + 2y = 20 →
  36. 36.3x + 2y = −29 and 5x − y = −31 →
  37. 37.3x − y = −15 and 2x + 4y = 18 →
  38. 38.2x + 7y = −44 and 7x + 2y = −19 →
  39. 39.7x + 5y = 62 and 5x + 7y = 58 →
  40. 40.8x + 6y = 108 and 6x + 8y = 102 →

Answer key

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

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