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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 129 · 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 + 6y = 36 →
  2. 2.x + 2y = 15 and 3x + 3y = 30 →
  3. 3.2x + 6y = 2 and x + y = −5 →
  4. 4.x − 4y = −4 and 3x + 6y = 42 →
  5. 5.6x + 5y = 3 and 3x − y = −30 →
  6. 6.9x + 7y = −102 and 7x + 9y = −90 →
  7. 7.6x + 4y = −40 and 5x + 3y = −34 →
  8. 8.6x + 2y = −58 and 2x + 2y = −22 →
  9. 9.x + 4y = 9 and 4x + y = 6 →
  10. 10.x + 2y = −13 and 2x + y = −17 →
  11. 11.7x + 3y = 11 and 3x + 7y = −1 →
  12. 12.x + y = 1 and x − 6y = 50 →
  13. 13.6x + 9y = 129 and 9x + 6y = 126 →
  14. 14.3x + 2y = 7 and 2x − 4y = 10 →
  15. 15.8x + 3y = −9 and 3x + 8y = 31 →
  16. 16.x + 5y = 1 and x − 5y = −9 →
  17. 17.3x + y = 2 and x − 4y = −21 →
  18. 18.5x + 3y = 5 and 3x − 2y = −16 →
  19. 19.x + 5y = 34 and 5x + 3y = 60 →
  20. 20.5x + 2y = 6 and x + 3y = −4 →
  21. 21.5x − y = 37 and x + 4y = −22 →
  22. 22.3x + 8y = 49 and 8x + 3y = 39 →
  23. 23.x − 3y = −8 and x + 6y = 1 →
  24. 24.2x + 6y = 58 and x + y = 11 →
  25. 25.6x + 2y = −2 and 2x + 6y = 10 →
  26. 26.6x + 8y = −14 and 8x + 6y = −42 →
  27. 27.7x + y = 49 and x + 7y = 55 →
  28. 28.4x + 3y = −24 and 3x + 4y = −11 →
  29. 29.2x − y = −15 and 4x + 2y = −10 →
  30. 30.x + y = 13 and 3x + 6y = 63 →
  31. 31.2x + 5y = −21 and 5x + y = −41 →
  32. 32.2x + 3y = −15 and 6x − y = −15 →
  33. 33.4x − 3y = 35 and 4x − y = 17 →
  34. 34.4x + 7y = 0 and 7x + 4y = −33 →
  35. 35.5x + 9y = 75 and 9x + 5y = 79 →
  36. 36.3x − 3y = 6 and x + 3y = −30 →
  37. 37.3x + 2y = 9 and 2x + 3y = 16 →
  38. 38.8x + 9y = 91 and 9x + 8y = 96 →
  39. 39.3x + y = 4 and 2x + 5y = −6 →
  40. 40.x + 5y = 1 and 5x + y = 29 →

Answer key

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

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