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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 82 · 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 − 3y = −8 and 3x + y = −14 →
  2. 2.6x + y = −13 and 3x + 5y = −11 →
  3. 3.2x + 8y = 90 and 8x + 2y = 90 →
  4. 4.6x + 5y = 52 and 6x − 3y = −12 →
  5. 5.3x − 3y = −15 and 6x + 3y = 33 →
  6. 6.8x + 5y = 109 and 5x + 8y = 112 →
  7. 7.3x + 5y = −2 and 2x + 6y = 4 →
  8. 8.x + 3y = 8 and 5x + y = −30 →
  9. 9.x + y = 11 and 2x − 5y = 8 →
  10. 10.4x − 3y = 17 and 6x − 5y = 25 →
  11. 11.3x + 6y = −36 and 3x + 3y = −15 →
  12. 12.3x + 5y = 34 and 3x + 2y = 28 →
  13. 13.6x + 3y = −39 and x + 5y = −38 →
  14. 14.4x + 5y = −17 and x + 3y = −20 →
  15. 15.4x + 8y = 44 and 8x + 4y = 28 →
  16. 16.3x + 6y = −15 and 5x − 6y = 71 →
  17. 17.3x − 2y = −4 and 6x + 6y = 42 →
  18. 18.x + 3y = 18 and 6x + 2y = 60 →
  19. 19.5x − 4y = −45 and x + y = 0 →
  20. 20.6x − 4y = 2 and 2x + 4y = −26 →
  21. 21.2x − 2y = 22 and 2x + 6y = −2 →
  22. 22.5x + 6y = 63 and 6x + 2y = 60 →
  23. 23.x + 6y = −31 and 5x + 3y = 7 →
  24. 24.x + 5y = 18 and 2x − 4y = 8 →
  25. 25.4x + 2y = 40 and 2x + 4y = 44 →
  26. 26.2x + 4y = −30 and 6x + y = −35 →
  27. 27.2x − 4y = −8 and 2x + y = 7 →
  28. 28.2x − 6y = −32 and 5x + 5y = 0 →
  29. 29.6x − 6y = 6 and 6x − 5y = 11 →
  30. 30.x + y = 11 and x − 5y = −37 →
  31. 31.2x + 4y = 26 and 2x + 3y = 24 →
  32. 32.x + 4y = 15 and 3x + 5y = 31 →
  33. 33.9x + 3y = 69 and 3x + 9y = 63 →
  34. 34.3x + 2y = 36 and 5x + y = 46 →
  35. 35.2x + 5y = −37 and x − 2y = 22 →
  36. 36.x + y = 12 and 4x + 6y = 62 →
  37. 37.2x − 2y = 8 and 2x + 2y = 20 →
  38. 38.7x + 2y = 18 and 2x + 7y = −27 →
  39. 39.4x + y = −29 and 2x + 3y = 3 →
  40. 40.6x + 2y = −70 and 3x − y = −19 →

Answer key

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

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