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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 356 · 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. 1.4x + y = 11 and 5x + 3y = 26 →
  2. 2.x + y = 0 and 6x + y = −45 →
  3. 3.x + 6y = −4 and 6x + y = 46 →
  4. 4.x + 5y = −12 and 4x − 3y = −2 →
  5. 5.x + 7y = 20 and 7x + y = 44 →
  6. 6.5x + 9y = 108 and 9x + 5y = 116 →
  7. 7.3x + 4y = −12 and 6x − y = −51 →
  8. 8.6x − y = −52 and 5x − 2y = −48 →
  9. 9.2x + 6y = 36 and 6x + 2y = 44 →
  10. 10.8x + 2y = −16 and 2x + 8y = 56 →
  11. 11.3x + 6y = −30 and 2x + 6y = −32 →
  12. 12.8x + y = −46 and x + 8y = 10 →
  13. 13.7x + 9y = 100 and 9x + 7y = 92 →
  14. 14.4x + 7y = −33 and 7x + 4y = 0 →
  15. 15.6x + 3y = 45 and 2x + 4y = 18 →
  16. 16.9x + 5y = −64 and 5x + 9y = −48 →
  17. 17.2x + 3y = 14 and 4x + 2y = 12 →
  18. 18.4x + 2y = 32 and 2x + 4y = 40 →
  19. 19.2x + 4y = 4 and 5x + 3y = −4 →
  20. 20.2x − 5y = 3 and 6x + 2y = 60 →
  21. 21.5x + y = 12 and 5x − y = 28 →
  22. 22.7x + 8y = −19 and 8x + 7y = −11 →
  23. 23.6x + 5y = 41 and x + 2y = 8 →
  24. 24.6x + 5y = −41 and 2x + 4y = −30 →
  25. 25.3x − y = −1 and 6x − 4y = 2 →
  26. 26.4x + 5y = 46 and 3x − 3y = 21 →
  27. 27.6x + 5y = 32 and 4x + y = 12 →
  28. 28.3x + 6y = −24 and 6x + 3y = 6 →
  29. 29.5x + 9y = −67 and 9x + 5y = −31 →
  30. 30.5x + 9y = 22 and 9x + 5y = 62 →
  31. 31.x + 2y = 12 and 2x + 2y = 18 →
  32. 32.2x + 3y = 5 and 4x + 3y = 19 →
  33. 33.x + 6y = −29 and x + y = 1 →
  34. 34.5x + 5y = 35 and 5x − 5y = 55 →
  35. 35.2x + 3y = 19 and 3x + 2y = 11 →
  36. 36.3x − y = −16 and 2x − 3y = −13 →
  37. 37.3x + 9y = 78 and 9x + 3y = 18 →
  38. 38.2x + 4y = −30 and 3x + 2y = −13 →
  39. 39.3x + 8y = 20 and 8x + 3y = −20 →
  40. 40.7x + 3y = −50 and 3x + 7y = −10 →

Answer key

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

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