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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 681 · 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 + 2y = 17 and 4x − y = 23 →
  2. 2.6x + 2y = −2 and 2x + y = 1 →
  3. 3.2x + 4y = −2 and 2x + 3y = −4 →
  4. 4.3x + 2y = 19 and 5x − 6y = 41 →
  5. 5.2x + y = 4 and x + 2y = 14 →
  6. 6.x − y = 13 and 5x + 2y = 16 →
  7. 7.4x + 3y = −14 and 6x − 5y = −40 →
  8. 8.5x + 4y = −3 and 2x + 5y = −8 →
  9. 9.9x + y = 33 and x + 9y = 57 →
  10. 10.9x + 3y = −15 and 3x + 9y = 3 →
  11. 11.2x + 5y = −35 and 5x + 2y = −35 →
  12. 12.6x + 4y = 18 and 2x − 4y = 54 →
  13. 13.6x + 5y = 21 and 5x + 6y = 34 →
  14. 14.x − 3y = 27 and 4x + 6y = −36 →
  15. 15.5x − 3y = 12 and 2x − y = 5 →
  16. 16.4x + 2y = 4 and 2x + 4y = −10 →
  17. 17.x − 3y = 12 and 6x + 6y = 0 →
  18. 18.x + 5y = −17 and 5x + y = 35 →
  19. 19.6x + 9y = −30 and 9x + 6y = −60 →
  20. 20.2x + 7y = −24 and 7x + 2y = 6 →
  21. 21.x − 6y = −22 and 4x + 5y = 57 →
  22. 22.4x + 4y = 12 and 4x − 2y = −18 →
  23. 23.4x + 3y = 41 and 3x + 4y = 36 →
  24. 24.4x + 2y = 28 and 2x + 4y = 2 →
  25. 25.4x − y = 16 and 4x + 2y = −8 →
  26. 26.6x + 2y = 48 and 5x + 5y = 70 →
  27. 27.6x + y = 16 and x + 2y = 10 →
  28. 28.6x + y = 24 and x + 6y = 39 →
  29. 29.x − y = 10 and 5x + 3y = 10 →
  30. 30.5x + 3y = −2 and 3x + 5y = −30 →
  31. 31.5x − 2y = −41 and 2x − 4y = −26 →
  32. 32.8x + 4y = −104 and 4x + 8y = −100 →
  33. 33.7x + 2y = 27 and 2x + 7y = 27 →
  34. 34.5x + 2y = 32 and 4x + y = 28 →
  35. 35.2x + y = 6 and 2x − y = 14 →
  36. 36.6x + 6y = −6 and x + 5y = 11 →
  37. 37.4x − 4y = −32 and 6x + 4y = 2 →
  38. 38.7x + 3y = 60 and 3x + 7y = 60 →
  39. 39.x + 8y = −47 and 8x + y = 65 →
  40. 40.6x + 3y = 9 and 4x + 6y = 2 →

Answer key

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

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