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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 847 · 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. 1.8x + 6y = −86 and 6x + 8y = −82 →
  2. 2.8x + 3y = −23 and 3x + 8y = 12 →
  3. 3.2x − 2y = 32 and 4x + 5y = −17 →
  4. 4.5x − 5y = −5 and 2x + 6y = 54 →
  5. 5.8x + y = 15 and x + 8y = 57 →
  6. 6.2x + 3y = −3 and 5x − 4y = −42 →
  7. 7.4x + 2y = 14 and 5x + 5y = 5 →
  8. 8.3x + 5y = 21 and 2x − 3y = −24 →
  9. 9.3x − 2y = 5 and 3x + 3y = 45 →
  10. 10.4x + 4y = 8 and 2x + 4y = 12 →
  11. 11.2x − 2y = 8 and 6x + 6y = −36 →
  12. 12.8x + y = 77 and x + 8y = 49 →
  13. 13.x + 6y = 28 and 6x + 3y = 3 →
  14. 14.4x − 5y = 72 and x + y = 0 →
  15. 15.5x + 6y = 99 and 6x + 4y = 90 →
  16. 16.5x + 3y = 17 and 2x + 6y = 26 →
  17. 17.2x + 3y = 4 and x + y = 1 →
  18. 18.7x + 3y = 31 and 3x + 7y = 59 →
  19. 19.6x + 5y = 69 and 3x + 6y = 45 →
  20. 20.2x + 3y = −33 and 3x + 2y = −32 →
  21. 21.2x + 6y = 46 and 2x − y = −3 →
  22. 22.5x + 2y = −6 and 6x + 6y = 0 →
  23. 23.9x + 3y = 54 and 3x + 9y = 42 →
  24. 24.x + 6y = 49 and 3x − 3y = −42 →
  25. 25.5x − 2y = −44 and 5x + y = −38 →
  26. 26.x + 5y = −44 and 4x + 3y = −40 →
  27. 27.3x − 5y = 8 and x − 6y = 20 →
  28. 28.4x + 9y = −79 and 9x + 4y = −64 →
  29. 29.2x + y = −10 and x − 5y = −27 →
  30. 30.9x + 7y = 26 and 7x + 9y = 38 →
  31. 31.2x + 6y = −42 and x + 2y = −17 →
  32. 32.3x + 4y = −30 and 2x − y = 2 →
  33. 33.5x − 2y = 28 and x + 2y = 20 →
  34. 34.4x + 9y = 40 and 9x + 4y = 25 →
  35. 35.3x − 4y = −37 and x − 5y = −27 →
  36. 36.2x + 5y = 7 and 5x − 3y = −29 →
  37. 37.6x + 8y = 38 and 8x + 6y = 32 →
  38. 38.x + 5y = 21 and x + 2y = 3 →
  39. 39.4x + 2y = −8 and 5x + y = 2 →
  40. 40.4x + y = 11 and x − 5y = −13 →

Answer key

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

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