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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 243 · 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 = 14 and 9x + y = 46 →
  2. 2.3x + 9y = −21 and 9x + 3y = 33 →
  3. 3.4x + y = 0 and x + 4y = −15 →
  4. 4.x + 6y = −9 and 6x + y = 16 →
  5. 5.6x − 3y = 72 and 3x − 6y = 63 →
  6. 6.6x − y = 15 and 2x − 5y = −9 →
  7. 7.3x + 4y = 31 and x + 2y = 11 →
  8. 8.5x + y = 41 and x + 2y = 1 →
  9. 9.3x − y = 5 and 2x + y = 0 →
  10. 10.4x + 6y = 54 and 6x + 4y = 66 →
  11. 11.4x + 3y = 45 and x + 5y = 24 →
  12. 12.2x − 5y = 21 and 6x + 3y = −27 →
  13. 13.x + y = 0 and 5x + 3y = 6 →
  14. 14.5x + 6y = −19 and x + 3y = −2 →
  15. 15.x − y = −2 and 2x + y = −22 →
  16. 16.7x + 9y = 10 and 9x + 7y = 22 →
  17. 17.2x − y = 11 and 5x − 6y = 3 →
  18. 18.x + y = 9 and x − 5y = −21 →
  19. 19.6x − y = 24 and 3x − 3y = −3 →
  20. 20.5x + y = 9 and 4x + 4y = 4 →
  21. 21.2x + 6y = −24 and 5x − 5y = −20 →
  22. 22.8x + 9y = −24 and 9x + 8y = −10 →
  23. 23.4x − 2y = −30 and 2x + 3y = 13 →
  24. 24.3x + 8y = −43 and 8x + 3y = 32 →
  25. 25.5x + 3y = 52 and 6x + y = 52 →
  26. 26.2x + 2y = 14 and x + 4y = 10 →
  27. 27.6x + y = −53 and 2x + 2y = −16 →
  28. 28.8x + 3y = −13 and 3x + 8y = 2 →
  29. 29.5x + 3y = −13 and 2x − 3y = −22 →
  30. 30.6x − 6y = 60 and x − 2y = 18 →
  31. 31.5x + 2y = 49 and 2x + 5y = 28 →
  32. 32.4x − 5y = −7 and 6x + 2y = 18 →
  33. 33.x + 5y = 22 and 4x − 6y = 10 →
  34. 34.5x − 3y = −29 and 3x − 5y = −27 →
  35. 35.7x + y = −33 and x + 7y = 57 →
  36. 36.2x + 9y = −59 and 9x + 2y = 4 →
  37. 37.3x + 3y = −9 and 5x + 3y = −7 →
  38. 38.2x + y = −7 and 2x + 2y = 0 →
  39. 39.6x − 2y = −24 and 5x + 4y = −37 →
  40. 40.5x − 2y = −41 and x + 5y = 35 →

Answer key

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

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