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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 594 · 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. 1.4x + y = 18 and 6x − 2y = 20 →
  2. 2.x + 3y = 30 and 2x + 2y = 28 →
  3. 3.5x − 6y = −5 and 5x − 4y = 5 →
  4. 4.x + 8y = −58 and 8x + y = 40 →
  5. 5.2x + 3y = 19 and 3x + 2y = 26 →
  6. 6.x − 6y = 45 and 4x + 4y = 12 →
  7. 7.7x + y = 20 and x + 7y = 44 →
  8. 8.5x + 6y = 58 and 6x + 5y = 52 →
  9. 9.3x + 2y = −29 and 3x + 6y = −33 →
  10. 10.7x + y = 47 and x + 7y = 41 →
  11. 11.x + 5y = 17 and 4x + 4y = −12 →
  12. 12.3x + y = −1 and x + 3y = −11 →
  13. 13.9x + 5y = −126 and 5x + 9y = −126 →
  14. 14.x + y = 2 and x + 2y = 9 →
  15. 15.2x − 6y = 26 and 6x − y = 27 →
  16. 16.6x + y = 51 and 2x − y = 13 →
  17. 17.5x + 4y = −38 and x + 4y = −14 →
  18. 18.4x + 3y = 1 and 2x + 4y = −2 →
  19. 19.7x + 8y = −19 and 8x + 7y = −11 →
  20. 20.3x + 7y = 60 and 7x + 3y = 60 →
  21. 21.6x + 5y = 38 and 4x + 5y = 22 →
  22. 22.2x − 5y = 19 and 6x + 2y = −28 →
  23. 23.6x + 6y = 30 and 5x − 5y = −45 →
  24. 24.9x + 3y = 48 and 3x + 9y = 48 →
  25. 25.x − 3y = −24 and x + 2y = 21 →
  26. 26.3x − 6y = 9 and 5x + 3y = 2 →
  27. 27.4x + 6y = 64 and 2x + 6y = 56 →
  28. 28.2x + 2y = −10 and 4x + 5y = −23 →
  29. 29.2x + 6y = −48 and 6x + 2y = −48 →
  30. 30.6x + 5y = −26 and 2x + 2y = −10 →
  31. 31.5x + 6y = 3 and 3x + 2y = −11 →
  32. 32.8x + 4y = 60 and 4x + 8y = 60 →
  33. 33.4x + 3y = 19 and x + y = 5 →
  34. 34.5x − 4y = 9 and 4x + 5y = 40 →
  35. 35.2x + 3y = −38 and 3x + 2y = −37 →
  36. 36.2x + 8y = 74 and 8x + 2y = 26 →
  37. 37.5x + 3y = 12 and x + y = 6 →
  38. 38.4x + 6y = 66 and 2x + 5y = 43 →
  39. 39.x + 5y = 8 and 6x + 4y = 22 →
  40. 40.8x + 4y = −20 and 4x + 8y = −16 →

Answer key

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

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