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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 38 · 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 + 7y = 65 and 7x + 9y = 47 →
  2. 2.2x − 4y = −26 and 5x − 2y = −41 →
  3. 3.2x + 6y = 26 and 2x + y = 1 →
  4. 4.8x + y = −57 and x + 8y = −15 →
  5. 5.x − 2y = 21 and 4x + 6y = −28 →
  6. 6.4x + y = 18 and x + 4y = 12 →
  7. 7.x + 6y = 38 and 6x + y = 18 →
  8. 8.6x + 4y = 10 and 4x + 6y = 10 →
  9. 9.9x + y = 10 and x + 9y = 10 →
  10. 10.x − y = 0 and 2x + 3y = −35 →
  11. 11.3x + 2y = −8 and 2x + 3y = −2 →
  12. 12.4x + 3y = −9 and 4x + 6y = −30 →
  13. 13.6x + y = −38 and 5x + 3y = −23 →
  14. 14.4x − y = 31 and 5x + 6y = 75 →
  15. 15.8x + 5y = −29 and 5x + 8y = −62 →
  16. 16.5x + 3y = 9 and 2x − 2y = 10 →
  17. 17.5x − 4y = 32 and 6x + 5y = 58 →
  18. 18.8x + 4y = 20 and 4x + 8y = 16 →
  19. 19.4x + 2y = −8 and 6x − y = −20 →
  20. 20.4x + 6y = −14 and 6x − 3y = 39 →
  21. 21.3x + 7y = −42 and 7x + 3y = −58 →
  22. 22.2x + y = 3 and x + 2y = 3 →
  23. 23.6x − 5y = −3 and x − y = −1 →
  24. 24.5x + y = 14 and x + 5y = −26 →
  25. 25.6x + 6y = −18 and 2x − 4y = 30 →
  26. 26.x + 2y = 9 and 6x + y = 32 →
  27. 27.x + 3y = 14 and 2x + y = 8 →
  28. 28.5x + 2y = 23 and 2x + 5y = 26 →
  29. 29.x + 3y = 14 and x − y = −6 →
  30. 30.4x − 2y = −2 and 4x + 4y = −20 →
  31. 31.2x + 3y = −11 and 3x + 2y = −19 →
  32. 32.5x + y = 1 and 4x − 5y = −34 →
  33. 33.5x + 2y = 23 and 2x + 5y = −16 →
  34. 34.2x − 5y = −12 and 6x + 4y = 2 →
  35. 35.2x − 6y = −6 and 6x + 4y = 26 →
  36. 36.6x + 4y = −18 and 4x + 2y = −8 →
  37. 37.6x − 6y = −48 and x − 6y = −43 →
  38. 38.5x − 2y = 58 and 5x + 2y = 22 →
  39. 39.3x − 6y = −30 and 6x + 5y = 59 →
  40. 40.4x + 4y = −20 and 3x + 2y = −8 →

Answer key

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

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