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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 458 · 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 + y = −11 and x + 3y = −1 →
  2. 2.5x − 2y = 29 and 2x + 4y = 2 →
  3. 3.6x + 4y = −24 and 4x + 6y = 4 →
  4. 4.x + 5y = 22 and 5x + y = 14 →
  5. 5.7x + 5y = 82 and 5x + 7y = 86 →
  6. 6.6x + 3y = −45 and 3x + 6y = −18 →
  7. 7.2x − y = 18 and 6x − y = 50 →
  8. 8.6x − 2y = 12 and 3x + 3y = 42 →
  9. 9.6x + y = −34 and x + 6y = −29 →
  10. 10.x − y = 13 and 4x + 2y = 4 →
  11. 11.9x + 2y = −41 and 2x + 9y = 8 →
  12. 12.4x − y = 21 and x − 4y = −6 →
  13. 13.x + 2y = 18 and 5x + 3y = 55 →
  14. 14.3x + y = 10 and 5x + 5y = 20 →
  15. 15.4x + 2y = 46 and 3x + y = 30 →
  16. 16.9x + 5y = 24 and 5x + 9y = −24 →
  17. 17.7x + y = 13 and x + 7y = −53 →
  18. 18.2x + 3y = −8 and 5x + y = −33 →
  19. 19.3x + 7y = 42 and 7x + 3y = 58 →
  20. 20.x − 5y = −34 and x − 3y = −18 →
  21. 21.x − 2y = 9 and 5x − 4y = −3 →
  22. 22.6x + 2y = 52 and 6x + 5y = 67 →
  23. 23.2x − 4y = −26 and 6x − 2y = −58 →
  24. 24.7x + 6y = −2 and 6x + 7y = −11 →
  25. 25.6x + y = −7 and 6x − 3y = −27 →
  26. 26.2x + 2y = −16 and 2x + 4y = −22 →
  27. 27.3x + 2y = −2 and 5x + y = 6 →
  28. 28.6x − 4y = 8 and 5x + 4y = 14 →
  29. 29.4x + 2y = −18 and 2x + 4y = 0 →
  30. 30.x + y = −6 and 3x − 2y = −28 →
  31. 31.2x + 4y = 18 and 4x + 2y = 0 →
  32. 32.2x + y = 5 and 5x − 3y = −37 →
  33. 33.5x + 2y = 13 and 4x − 3y = 15 →
  34. 34.2x + y = −1 and x + 2y = 1 →
  35. 35.2x − 4y = −18 and 6x − 3y = −18 →
  36. 36.3x + 2y = 33 and 2x + 3y = 37 →
  37. 37.5x + 7y = 80 and 7x + 5y = 88 →
  38. 38.2x + 6y = 10 and x + 6y = 8 →
  39. 39.2x + 4y = 34 and 3x + 5y = 44 →
  40. 40.4x + 5y = −6 and 2x − y = 4 →

Answer key

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

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