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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 58 · 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 − 5y = −11 and x − 6y = −34 →
  2. 2.3x + y = 23 and 3x + 3y = 33 →
  3. 3.4x + 2y = −10 and x − 5y = −30 →
  4. 4.6x + 5y = −11 and 5x + 6y = −22 →
  5. 5.4x + y = 12 and 5x + 6y = 53 →
  6. 6.9x + 2y = −34 and 2x + 9y = −76 →
  7. 7.4x + 2y = 2 and 6x + 2y = 4 →
  8. 8.5x − 3y = 19 and 6x + 2y = 34 →
  9. 9.x + 5y = −20 and 2x − 2y = −4 →
  10. 10.9x + 8y = −48 and 8x + 9y = −37 →
  11. 11.2x + 4y = −32 and 4x + 2y = −28 →
  12. 12.9x + 3y = −33 and 3x + 9y = 21 →
  13. 13.6x + 5y = −63 and x + 5y = −48 →
  14. 14.5x + 3y = 47 and 2x + 4y = 30 →
  15. 15.3x + 5y = 47 and 5x + 3y = 41 →
  16. 16.3x + y = 14 and 2x + 5y = −8 →
  17. 17.2x + y = −3 and 6x + 4y = −6 →
  18. 18.5x + 3y = 55 and 2x − 4y = −4 →
  19. 19.x + 3y = 28 and 3x + y = 28 →
  20. 20.4x + y = 1 and 3x + y = 2 →
  21. 21.5x + 2y = −14 and 2x + 5y = 28 →
  22. 22.3x + 3y = −27 and x + 5y = −21 →
  23. 23.6x + 2y = 38 and 5x + y = 37 →
  24. 24.5x + 3y = 58 and 5x + y = 46 →
  25. 25.5x + y = −29 and x + 5y = −1 →
  26. 26.5x + 5y = −40 and 5x − 4y = −22 →
  27. 27.4x + 6y = 50 and 6x + 4y = 50 →
  28. 28.3x − y = −21 and 2x − 4y = 6 →
  29. 29.5x − 3y = 8 and 4x − 3y = 7 →
  30. 30.9x + 5y = −102 and 5x + 9y = −94 →
  31. 31.6x + 5y = 63 and 5x − 5y = 25 →
  32. 32.6x + y = 20 and 3x + y = 11 →
  33. 33.6x + 9y = 102 and 9x + 6y = 108 →
  34. 34.3x + 2y = 24 and 2x + 3y = 31 →
  35. 35.3x − 5y = −36 and x + 6y = 57 →
  36. 36.4x + 4y = 12 and 2x + 6y = −18 →
  37. 37.6x + 9y = −111 and 9x + 6y = −99 →
  38. 38.6x + y = 39 and 6x + 3y = 57 →
  39. 39.x − 3y = −15 and 4x + 4y = 52 →
  40. 40.2x − 5y = −17 and 5x + 5y = 45 →

Answer key

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

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