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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 911 · 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. 1.3x + 2y = 29 and 2x + 3y = 31 →
  2. 2.x + 3y = −23 and 3x + y = −5 →
  3. 3.4x − 3y = 27 and 6x − 5y = 39 →
  4. 4.3x + 4y = 27 and 2x − 2y = 4 →
  5. 5.5x + 7y = 74 and 7x + 5y = 70 →
  6. 6.x + 4y = −22 and 6x + 6y = −42 →
  7. 7.x + 2y = 3 and x − 4y = −21 →
  8. 8.x + 2y = −10 and 2x + y = 1 →
  9. 9.4x − y = −29 and 2x − 2y = −28 →
  10. 10.5x + 2y = 10 and 2x + 5y = −17 →
  11. 11.3x + 4y = −30 and 3x + 3y = −21 →
  12. 12.5x + 3y = −41 and x − 2y = −3 →
  13. 13.4x + 6y = 22 and 6x + 5y = 37 →
  14. 14.5x + 4y = 30 and x + 2y = 12 →
  15. 15.2x + 5y = −49 and 3x + y = −28 →
  16. 16.x − 2y = 12 and x + 3y = −3 →
  17. 17.5x + 7y = −47 and 7x + 5y = −61 →
  18. 18.6x + y = −35 and 4x + 3y = −21 →
  19. 19.6x + 4y = 20 and 5x − 4y = 2 →
  20. 20.2x + 4y = −40 and 4x + 2y = −38 →
  21. 21.3x + 5y = −13 and 5x + 3y = 5 →
  22. 22.9x + 5y = 97 and 5x + 9y = 85 →
  23. 23.9x + 3y = −51 and 3x + 9y = −57 →
  24. 24.6x − y = 51 and 4x + 6y = 54 →
  25. 25.2x + 5y = 38 and x + y = 10 →
  26. 26.2x − 6y = −22 and 2x − y = −7 →
  27. 27.5x + 5y = −40 and x − 6y = 20 →
  28. 28.2x − 3y = −14 and 5x + 4y = 57 →
  29. 29.5x + 6y = −47 and 3x + y = −23 →
  30. 30.5x + 6y = −25 and x + 6y = −29 →
  31. 31.5x − 5y = −60 and x + 2y = 12 →
  32. 32.3x + y = 27 and 3x − y = 21 →
  33. 33.6x − 4y = 32 and x − 2y = 0 →
  34. 34.6x − 2y = 32 and x − y = 2 →
  35. 35.5x + 3y = −3 and 2x − y = −10 →
  36. 36.2x + 4y = −30 and 4x + 2y = −24 →
  37. 37.8x + 5y = −57 and 5x + 8y = −21 →
  38. 38.x + 5y = 10 and 5x + y = 26 →
  39. 39.8x + 4y = 56 and 4x + 8y = 64 →
  40. 40.2x − y = 0 and 5x − 4y = 6 →

Answer key

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

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