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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 143 · 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.x + 9y = 20 and 9x + y = 20 →
  2. 2.4x − 3y = 37 and 5x + 4y = 23 →
  3. 3.3x − 4y = 3 and 5x − 4y = 13 →
  4. 4.5x − 5y = 15 and x + 6y = 10 →
  5. 5.5x + 4y = 22 and 3x + 3y = 12 →
  6. 6.4x + 5y = 25 and 4x − 6y = 14 →
  7. 7.9x + 3y = −15 and 3x + 9y = −69 →
  8. 8.2x + y = −12 and x + 2y = −18 →
  9. 9.x + 5y = 39 and 5x + 2y = −12 →
  10. 10.x − 5y = 27 and x − 6y = 31 →
  11. 11.6x − 5y = −38 and 3x + 4y = −32 →
  12. 12.6x + 3y = −21 and 5x − 4y = −11 →
  13. 13.x + 7y = 62 and 7x + y = 50 →
  14. 14.8x + 2y = 14 and 2x + 8y = 26 →
  15. 15.5x + 4y = 58 and 6x + 3y = 57 →
  16. 16.2x + 5y = −21 and x + 4y = −15 →
  17. 17.6x + y = 10 and 2x + 4y = −4 →
  18. 18.4x − 6y = −8 and 3x − 3y = 3 →
  19. 19.4x + y = 41 and 5x + 6y = 94 →
  20. 20.5x + y = −38 and x + 5y = 26 →
  21. 21.4x + 2y = −8 and 2x + 6y = 6 →
  22. 22.7x + 9y = 60 and 9x + 7y = 68 →
  23. 23.6x + 5y = 40 and 2x + 2y = 14 →
  24. 24.4x + 2y = 42 and x + 4y = 35 →
  25. 25.2x + y = 0 and x + 2y = −3 →
  26. 26.2x − 5y = 2 and 5x − 4y = 22 →
  27. 27.x + y = 9 and x + 5y = 41 →
  28. 28.2x + 6y = 54 and 2x − 4y = −26 →
  29. 29.x + 2y = −6 and x + 5y = −18 →
  30. 30.5x + 2y = 43 and 3x + 3y = 42 →
  31. 31.2x + y = 16 and 3x + 2y = 23 →
  32. 32.6x − 5y = 49 and 4x + 2y = 38 →
  33. 33.x + 5y = 11 and 5x + 6y = 36 →
  34. 34.5x + y = 16 and x + 5y = 8 →
  35. 35.2x + y = −11 and 6x + y = −35 →
  36. 36.2x + 6y = 48 and 6x + 2y = 48 →
  37. 37.5x − 3y = 29 and x + 2y = 11 →
  38. 38.6x − 5y = −19 and 4x − 5y = −21 →
  39. 39.2x − y = 21 and 2x + 3y = 9 →
  40. 40.4x − 2y = −20 and 3x + 5y = 11 →

Answer key

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

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