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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 954 · 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. 1.2x − y = 0 and 4x + 6y = 48 →
  2. 2.4x − 3y = 53 and 5x − 6y = 82 →
  3. 3.6x + 3y = 36 and 6x − 3y = 0 →
  4. 4.3x + y = −14 and x − 3y = −28 →
  5. 5.8x + 6y = 68 and 6x + 8y = 72 →
  6. 6.5x + 3y = 35 and 3x + 5y = 37 →
  7. 7.5x + 9y = 99 and 9x + 5y = 111 →
  8. 8.x + 3y = 22 and x + y = 8 →
  9. 9.6x + 4y = 44 and 4x − 6y = 12 →
  10. 10.2x + y = −11 and 6x + 4y = −38 →
  11. 11.5x − y = 43 and 4x + y = 38 →
  12. 12.2x + 6y = 0 and 5x − 5y = −20 →
  13. 13.8x + 7y = 34 and 7x + 8y = 26 →
  14. 14.4x + 2y = 20 and 2x + 5y = 18 →
  15. 15.3x + 2y = 41 and 2x + 4y = 46 →
  16. 16.x + 3y = 0 and x + y = −2 →
  17. 17.3x + 5y = −2 and 4x + 2y = 16 →
  18. 18.6x + 5y = 70 and 6x − 2y = 14 →
  19. 19.6x + y = −41 and 4x − 5y = 1 →
  20. 20.x + 8y = 9 and 8x + y = 9 →
  21. 21.9x + 6y = −39 and 6x + 9y = −6 →
  22. 22.4x + y = −6 and x + 2y = 2 →
  23. 23.4x + 6y = −16 and 6x + 4y = 16 →
  24. 24.6x + y = 10 and 6x + 2y = 14 →
  25. 25.x − 2y = 2 and 4x − y = −20 →
  26. 26.4x + 2y = 32 and 5x + 3y = 44 →
  27. 27.x − 2y = 15 and 6x + 3y = 0 →
  28. 28.8x + y = 14 and x + 8y = 49 →
  29. 29.4x − 4y = 0 and x − 6y = −10 →
  30. 30.5x − y = 39 and 2x − 3y = 13 →
  31. 31.2x + 6y = 18 and 3x + y = −5 →
  32. 32.6x + 8y = 14 and 8x + 6y = −14 →
  33. 33.3x + y = −11 and x + y = −3 →
  34. 34.x − 2y = 16 and 5x + 6y = −64 →
  35. 35.6x + y = 3 and 6x − 2y = −24 →
  36. 36.3x + 5y = −38 and 5x + 3y = −42 →
  37. 37.5x + 2y = 34 and 4x − 2y = 2 →
  38. 38.5x + 4y = 19 and 4x + 5y = 17 →
  39. 39.4x + 3y = 25 and 4x − 2y = −10 →
  40. 40.5x + 5y = 60 and 3x + y = 20 →

Answer key

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

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