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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 231 · 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 2x − 6y = −26 →
  2. 2.2x + y = 11 and 4x + 5y = 49 →
  3. 3.5x + 6y = −26 and 6x + 5y = −29 →
  4. 4.2x + 6y = 68 and 4x + 6y = 82 →
  5. 5.6x + 5y = −9 and 4x − 5y = −31 →
  6. 6.3x − 6y = −66 and 2x + 4y = 12 →
  7. 7.8x + 4y = 4 and 4x + 8y = 20 →
  8. 8.3x + 3y = 15 and 5x + 2y = −2 →
  9. 9.5x + 4y = 58 and 6x + 4y = 64 →
  10. 10.3x + y = 36 and x + 3y = 36 →
  11. 11.x + 2y = 17 and 2x + y = 22 →
  12. 12.3x + 5y = −7 and 4x + y = −15 →
  13. 13.x − 6y = 15 and 5x − 3y = 21 →
  14. 14.5x + 5y = −30 and 4x + 6y = −42 →
  15. 15.x + 3y = 8 and 5x + 5y = 30 →
  16. 16.5x + 4y = −53 and 4x + 5y = −55 →
  17. 17.3x + 5y = −52 and 3x − 5y = −2 →
  18. 18.4x + y = 36 and x + 4y = 39 →
  19. 19.4x + 8y = 40 and 8x + 4y = 44 →
  20. 20.6x − y = −33 and 3x + 4y = −30 →
  21. 21.8x + y = 80 and x + 8y = 73 →
  22. 22.3x − 5y = −47 and 2x + 3y = 13 →
  23. 23.x + 3y = −12 and x − 4y = 37 →
  24. 24.4x − 6y = −42 and 4x + 5y = −31 →
  25. 25.6x − 5y = 1 and 5x + 6y = 72 →
  26. 26.x − 6y = 7 and 5x + 4y = −33 →
  27. 27.2x + 3y = −5 and 6x + 6y = −12 →
  28. 28.2x + 4y = −22 and 2x + 5y = −24 →
  29. 29.x + y = 6 and x + 5y = 38 →
  30. 30.3x + 9y = −24 and 9x + 3y = 0 →
  31. 31.x + y = −6 and x − 3y = −18 →
  32. 32.2x + 3y = 15 and 3x + y = −9 →
  33. 33.2x + 7y = 12 and 7x + 2y = −48 →
  34. 34.7x + 6y = 68 and 6x + 7y = 62 →
  35. 35.3x − y = −1 and 3x − 2y = −5 →
  36. 36.4x + 2y = 38 and 2x + 4y = 34 →
  37. 37.4x − 3y = −5 and x + 3y = 10 →
  38. 38.6x + 4y = 28 and 4x + 6y = 22 →
  39. 39.4x + 3y = 35 and 3x + 4y = 42 →
  40. 40.5x + 4y = 63 and 3x + 4y = 49 →

Answer key

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

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