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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 2 · 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 + 6y = −9 and 6x + 3y = −45 →
  2. 2.5x + 5y = 70 and x − 6y = −49 →
  3. 3.4x + 6y = 50 and 3x + 6y = 48 →
  4. 4.3x − 3y = −42 and 5x + 6y = 18 →
  5. 5.6x + 3y = 0 and 5x + 5y = 10 →
  6. 6.x + 5y = −5 and 5x + y = 23 →
  7. 7.3x + 5y = 11 and 2x + 5y = 9 →
  8. 8.5x + 2y = 37 and 5x − 5y = −5 →
  9. 9.6x + 4y = 42 and 4x + 6y = 38 →
  10. 10.4x + 5y = 39 and 5x + 4y = 42 →
  11. 11.5x + 4y = 47 and 4x − 6y = 10 →
  12. 12.6x + 5y = 7 and 5x + 6y = −7 →
  13. 13.7x + 2y = 1 and 2x + 7y = −19 →
  14. 14.6x + 5y = 69 and x − y = −5 →
  15. 15.6x − y = 11 and 2x + 3y = 7 →
  16. 16.4x + 5y = 3 and 5x + 3y = −6 →
  17. 17.2x + 4y = 8 and 4x + y = −12 →
  18. 18.2x − 5y = 11 and 5x + y = 14 →
  19. 19.5x + 2y = 7 and 2x + 5y = 7 →
  20. 20.5x − 6y = 16 and x + 5y = 28 →
  21. 21.3x + 6y = 3 and x + 6y = −7 →
  22. 22.6x + y = 56 and 2x + 5y = 28 →
  23. 23.2x + 9y = 82 and 9x + 2y = 61 →
  24. 24.x − 6y = −8 and 2x + y = −3 →
  25. 25.6x + 2y = 30 and 6x − y = 21 →
  26. 26.4x + 2y = 14 and x − 3y = −28 →
  27. 27.3x − 2y = 11 and 5x + 4y = 77 →
  28. 28.5x + 2y = 12 and 6x − 5y = 44 →
  29. 29.x − 3y = −10 and 5x − 4y = −6 →
  30. 30.x + 6y = 35 and 4x − 3y = −49 →
  31. 31.4x + 7y = −32 and 7x + 4y = 10 →
  32. 32.3x + 7y = 60 and 7x + 3y = 20 →
  33. 33.9x + 6y = −93 and 6x + 9y = −87 →
  34. 34.5x + 4y = 39 and 2x + 4y = 18 →
  35. 35.6x + y = 11 and 4x + 2y = 6 →
  36. 36.9x + y = −41 and x + 9y = 31 →
  37. 37.3x − 4y = 4 and 2x − y = 6 →
  38. 38.7x + 9y = 99 and 9x + 7y = 109 →
  39. 39.4x + 5y = 56 and 3x − 6y = 3 →
  40. 40.7x + 9y = 30 and 9x + 7y = 2 →

Answer key

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

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