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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 221 · 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 + 5y = 21 and 5x + 3y = 19 →
  2. 2.x + 4y = −22 and 4x + y = −13 →
  3. 3.2x + y = 17 and x + 2y = 16 →
  4. 4.4x + 3y = 12 and 3x + 4y = −5 →
  5. 5.2x − 6y = −4 and 4x − 6y = 10 →
  6. 6.6x + 5y = −1 and 6x + 6y = −6 →
  7. 7.x + 6y = 33 and 5x + 3y = 30 →
  8. 8.x + 5y = 37 and 5x − 4y = −47 →
  9. 9.5x + y = −6 and 2x + y = −3 →
  10. 10.x − 2y = 0 and 4x − y = 14 →
  11. 11.2x + 6y = −40 and 6x + 2y = −8 →
  12. 12.x + 7y = 13 and 7x + y = −5 →
  13. 13.5x + 4y = 23 and x + y = 4 →
  14. 14.6x + 8y = 18 and 8x + 6y = −18 →
  15. 15.6x + 7y = 25 and 7x + 6y = 27 →
  16. 16.6x − 5y = 63 and 2x + 3y = −21 →
  17. 17.2x − 5y = −4 and 4x + 2y = 16 →
  18. 18.2x + 4y = −10 and 4x + 2y = −32 →
  19. 19.x + 5y = 18 and 5x + y = 18 →
  20. 20.2x − y = −9 and 3x + y = −11 →
  21. 21.x + 3y = 9 and 4x − y = 10 →
  22. 22.3x + 6y = 66 and 6x + 3y = 51 →
  23. 23.7x + 3y = −7 and 3x + 7y = 37 →
  24. 24.2x + 3y = 11 and 4x + 5y = 19 →
  25. 25.2x + 4y = 24 and 5x − 3y = 34 →
  26. 26.3x − 4y = 33 and x − 6y = 39 →
  27. 27.5x + 4y = −41 and 4x + y = −13 →
  28. 28.x + 5y = −29 and 2x + y = 5 →
  29. 29.4x + y = −26 and 5x + y = −33 →
  30. 30.2x + y = 21 and x + 2y = 21 →
  31. 31.6x + 5y = 79 and 5x + 6y = 75 →
  32. 32.3x + 3y = 15 and 6x + 5y = 27 →
  33. 33.3x − 2y = −25 and x + 3y = −1 →
  34. 34.2x + 5y = −33 and 5x + 2y = −30 →
  35. 35.5x + 6y = 59 and x − 2y = −1 →
  36. 36.4x + y = 5 and 5x + 3y = 1 →
  37. 37.3x − 3y = −30 and 2x − 5y = −26 →
  38. 38.3x + 9y = −30 and 9x + 3y = −18 →
  39. 39.5x + 2y = 19 and 2x + 5y = −26 →
  40. 40.5x + 9y = 68 and 9x + 5y = 44 →

Answer key

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

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