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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 42 · 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 + 7y = 47 and 7x + y = −55 →
  2. 2.4x + 6y = −16 and 6x + 4y = −34 →
  3. 3.5x + 3y = 16 and 4x + 6y = 2 →
  4. 4.x − y = 1 and 3x − 4y = 0 →
  5. 5.5x + 2y = 39 and 2x + 5y = 24 →
  6. 6.4x − 6y = 24 and 2x + 4y = 26 →
  7. 7.6x + 5y = 79 and 4x − 2y = 26 →
  8. 8.x + 5y = −28 and 6x + 6y = −72 →
  9. 9.2x + 3y = 17 and 6x + y = 11 →
  10. 10.3x + 8y = 57 and 8x + 3y = 42 →
  11. 11.3x + 4y = −45 and x + 3y = −30 →
  12. 12.x + 8y = 11 and 8x + y = −38 →
  13. 13.x + 3y = 7 and 2x − 6y = −46 →
  14. 14.2x + y = 11 and x + 2y = 13 →
  15. 15.6x + 2y = −14 and 5x + 3y = −17 →
  16. 16.3x + 7y = −41 and 7x + 3y = 11 →
  17. 17.4x − 6y = 70 and x − 6y = 49 →
  18. 18.x − 3y = −19 and 4x + y = 2 →
  19. 19.x − 2y = −13 and 3x − y = −14 →
  20. 20.3x + 9y = −42 and 9x + 3y = −78 →
  21. 21.2x + 5y = 28 and 5x + 6y = 44 →
  22. 22.4x − 3y = −24 and 5x + 4y = 1 →
  23. 23.6x + 4y = 4 and 5x + 4y = 2 →
  24. 24.x + y = 2 and 4x + y = 17 →
  25. 25.7x + 4y = 14 and 4x + 7y = 41 →
  26. 26.8x + 3y = 39 and 3x + 8y = 49 →
  27. 27.8x + y = −37 and x + 8y = −44 →
  28. 28.4x + 7y = 12 and 7x + 4y = −12 →
  29. 29.2x − 5y = −4 and 6x + 6y = 72 →
  30. 30.x + y = −3 and 3x − 6y = 54 →
  31. 31.5x + 6y = 74 and x + 3y = 31 →
  32. 32.2x + y = −9 and 2x − 4y = −14 →
  33. 33.3x + 7y = −1 and 7x + 3y = 11 →
  34. 34.2x − 3y = 8 and 4x + 5y = −50 →
  35. 35.7x + 6y = 97 and 6x + 7y = 98 →
  36. 36.5x + y = 43 and 4x + 3y = 41 →
  37. 37.3x + 9y = −90 and 9x + 3y = −78 →
  38. 38.2x − y = 26 and x + 2y = −7 →
  39. 39.4x + 5y = −23 and 3x − 5y = 9 →
  40. 40.4x + y = 20 and 3x + 2y = 20 →

Answer key

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

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