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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 248 · 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. 1.2x + 4y = 12 and 4x + 2y = −18 →
  2. 2.2x + 6y = 28 and 6x − 6y = −12 →
  3. 3.x + 4y = 3 and 4x + y = −33 →
  4. 4.3x + y = 4 and 5x + 3y = 4 →
  5. 5.5x + 6y = 52 and 4x − 2y = −6 →
  6. 6.6x + y = 44 and 2x + 2y = 18 →
  7. 7.3x + 3y = −48 and 3x + y = −30 →
  8. 8.3x + 4y = −6 and 3x + 6y = −18 →
  9. 9.4x − 4y = 0 and x + y = 2 →
  10. 10.5x − y = 6 and 2x + y = 1 →
  11. 11.5x + 6y = 19 and 6x − 4y = 34 →
  12. 12.2x + 4y = −4 and 4x + 2y = −20 →
  13. 13.7x + 8y = 84 and 8x + 7y = 81 →
  14. 14.x − y = 9 and 2x + 3y = −7 →
  15. 15.7x + 8y = 47 and 8x + 7y = 58 →
  16. 16.6x + 4y = 10 and 2x + 2y = 4 →
  17. 17.3x + 6y = 75 and 6x + 4y = 86 →
  18. 18.5x − 6y = 23 and 2x + 4y = 22 →
  19. 19.8x + 2y = 38 and 2x + 8y = 62 →
  20. 20.5x + 6y = −55 and 6x + 5y = −55 →
  21. 21.x + 5y = 26 and 5x + y = 10 →
  22. 22.2x + 5y = 53 and 4x + 6y = 70 →
  23. 23.8x + 3y = 87 and 3x + 8y = 67 →
  24. 24.6x + 6y = 6 and 5x + 3y = −3 →
  25. 25.3x + y = 22 and x + 3y = −6 →
  26. 26.4x − 5y = −40 and 3x + y = −11 →
  27. 27.2x + 5y = 26 and 5x − 4y = −67 →
  28. 28.6x + y = 60 and 3x + 4y = 51 →
  29. 29.2x − 2y = 0 and 3x − 4y = −4 →
  30. 30.5x + 2y = −52 and 5x + 6y = −76 →
  31. 31.x + y = −15 and 5x − 2y = −26 →
  32. 32.7x + y = 50 and x + 7y = 14 →
  33. 33.3x + 8y = 23 and 8x + 3y = 43 →
  34. 34.x + 4y = −21 and 4x + y = 21 →
  35. 35.5x + 6y = −3 and 5x − 3y = −66 →
  36. 36.4x + 5y = −28 and x + 5y = −37 →
  37. 37.x − 5y = −7 and 5x − 4y = 7 →
  38. 38.5x − 2y = −6 and x − 4y = −30 →
  39. 39.6x − y = 13 and x + 4y = −2 →
  40. 40.2x + 7y = 67 and 7x + 2y = 32 →

Answer key

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

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