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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 675 · 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. 1.6x + 7y = −43 and 7x + 6y = −35 →
  2. 2.4x − 3y = −5 and 5x + y = −11 →
  3. 3.4x + 5y = −29 and 4x + y = −25 →
  4. 4.2x − 2y = 0 and x + 5y = 12 →
  5. 5.3x − y = −26 and 2x + y = −4 →
  6. 6.6x + 3y = 45 and 5x + 4y = 51 →
  7. 7.4x + 3y = 38 and 3x + 4y = 32 →
  8. 8.4x + 2y = −10 and 6x + 2y = −16 →
  9. 9.7x + 9y = 44 and 9x + 7y = 52 →
  10. 10.x − 6y = 41 and 4x + 6y = −16 →
  11. 11.6x + y = 56 and x + 6y = 56 →
  12. 12.2x − 2y = 4 and 4x − 3y = 14 →
  13. 13.2x + 6y = 60 and 3x − 3y = 6 →
  14. 14.x + y = 7 and x − y = 1 →
  15. 15.3x + 4y = −9 and x + 5y = 8 →
  16. 16.5x + 4y = −23 and 4x + 5y = −31 →
  17. 17.5x − 4y = −7 and x + 5y = 45 →
  18. 18.2x + 6y = 38 and 2x − y = −4 →
  19. 19.3x + 6y = 0 and 6x + 3y = −27 →
  20. 20.7x + y = −53 and x + 7y = −35 →
  21. 21.x − 3y = 4 and 4x + 6y = −2 →
  22. 22.3x + y = 18 and x + 3y = 30 →
  23. 23.5x + 2y = −1 and 3x + 2y = 1 →
  24. 24.5x − 3y = 20 and 5x + 6y = 65 →
  25. 25.6x + 7y = 63 and 7x + 6y = 67 →
  26. 26.5x − 2y = −28 and 2x + 6y = 50 →
  27. 27.6x + 4y = −54 and 5x − 6y = 39 →
  28. 28.3x + 3y = −48 and 2x + 4y = −48 →
  29. 29.6x + 2y = 64 and 6x + 5y = 88 →
  30. 30.3x − 4y = 33 and 2x + 5y = −47 →
  31. 31.7x + 4y = 48 and 4x + 7y = 18 →
  32. 32.4x + 3y = 29 and 3x + 4y = 34 →
  33. 33.7x + 2y = 23 and 2x + 7y = 58 →
  34. 34.8x + y = −53 and x + 8y = 17 →
  35. 35.8x + 2y = 30 and 2x + 8y = 60 →
  36. 36.x + 2y = 5 and 5x + 2y = −7 →
  37. 37.2x − 3y = −8 and 6x + 3y = 24 →
  38. 38.5x + 9y = 4 and 9x + 5y = −4 →
  39. 39.3x − 4y = −19 and x − 4y = −25 →
  40. 40.6x + 2y = −10 and 3x + 5y = −1 →

Answer key

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

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