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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 1 · 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 + 4y = −4 and 5x − 5y = −25 →
  2. 2.2x − y = −4 and 4x + 5y = 48 →
  3. 3.3x + y = 14 and x − 6y = −27 →
  4. 4.8x + 5y = −72 and 5x + 8y = −84 →
  5. 5.6x + 7y = −20 and 7x + 6y = −6 →
  6. 6.6x − 3y = −72 and 6x − 5y = −88 →
  7. 7.3x + 2y = 25 and 6x + 2y = 46 →
  8. 8.6x + 3y = 21 and 2x + 5y = −13 →
  9. 9.2x − 6y = −18 and 3x + 4y = 38 →
  10. 10.6x + 5y = 29 and 5x + 6y = 26 →
  11. 11.2x + 8y = 30 and 8x + 2y = −60 →
  12. 12.2x + 4y = 48 and 5x + 5y = 75 →
  13. 13.9x + y = 49 and x + 9y = 41 →
  14. 14.x − 5y = −48 and 5x + 2y = 3 →
  15. 15.2x + 5y = 16 and 5x + 2y = 19 →
  16. 16.2x + 4y = −6 and 4x + 2y = −18 →
  17. 17.5x + y = 15 and 6x − 3y = −3 →
  18. 18.5x + 4y = 53 and 4x + 5y = 46 →
  19. 19.8x + 5y = 44 and 5x + 8y = 47 →
  20. 20.3x + 3y = 30 and x + 6y = 50 →
  21. 21.5x + y = −12 and 3x + 6y = −45 →
  22. 22.2x + 7y = −30 and 7x + 2y = −60 →
  23. 23.7x + 6y = −31 and 6x + 7y = −21 →
  24. 24.3x − 6y = 12 and 4x − 3y = 26 →
  25. 25.x + y = 6 and 3x − 4y = 4 →
  26. 26.6x + 5y = −21 and 2x + 3y = −11 →
  27. 27.3x + y = 11 and x + 3y = −15 →
  28. 28.x + 4y = 29 and 5x + 5y = 40 →
  29. 29.4x + 3y = −22 and 4x − y = −14 →
  30. 30.x + 4y = 29 and x − 2y = −1 →
  31. 31.2x + 5y = −37 and x + 5y = −41 →
  32. 32.4x + 7y = 43 and 7x + 4y = 34 →
  33. 33.8x + 3y = −58 and 3x + 8y = −8 →
  34. 34.2x + 4y = 46 and 4x + 2y = 38 →
  35. 35.5x − 4y = −13 and x − 6y = −13 →
  36. 36.5x + y = 24 and x + 5y = −24 →
  37. 37.x + 2y = −11 and x + 5y = −23 →
  38. 38.7x + y = 55 and x + 7y = 49 →
  39. 39.x + 3y = 0 and 4x + y = 33 →
  40. 40.2x + 3y = −3 and 4x − y = −13 →

Answer key

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

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