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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 822 · 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. 1.5x − 6y = −1 and 2x + y = 3 →
  2. 2.7x + 9y = −84 and 9x + 7y = −76 →
  3. 3.6x + 4y = 8 and 5x + y = 23 →
  4. 4.x − y = 5 and x + 5y = 11 →
  5. 5.x − 4y = 31 and 3x + 2y = −5 →
  6. 6.9x + 2y = 78 and 2x + 9y = 43 →
  7. 7.x + 6y = 56 and 6x + y = 21 →
  8. 8.6x + 6y = −24 and 2x + 5y = −29 →
  9. 9.7x + 8y = 30 and 8x + 7y = 30 →
  10. 10.3x + 4y = 18 and 5x − 2y = 4 →
  11. 11.6x + 4y = −30 and 4x − 4y = 20 →
  12. 12.2x + 2y = 22 and 5x − 2y = 34 →
  13. 13.8x + 2y = 26 and 2x + 8y = 14 →
  14. 14.3x + y = 21 and 2x − 4y = −14 →
  15. 15.6x + 4y = 64 and 6x + 2y = 50 →
  16. 16.4x + 4y = −12 and 4x − 2y = −18 →
  17. 17.6x + 2y = 66 and 3x + 5y = 69 →
  18. 18.7x + y = 58 and x + 7y = 70 →
  19. 19.3x + 8y = 49 and 8x + 3y = 39 →
  20. 20.5x + 4y = −4 and 4x + 5y = −14 →
  21. 21.5x − 4y = −34 and 2x + 6y = −6 →
  22. 22.2x − 2y = 28 and 6x − 5y = 77 →
  23. 23.2x + 5y = −15 and 2x − y = 15 →
  24. 24.4x + 5y = 72 and 5x + y = 48 →
  25. 25.x + 3y = −27 and 3x − 2y = 7 →
  26. 26.2x + 2y = 24 and 5x − 3y = −12 →
  27. 27.8x + 6y = 44 and 6x + 8y = 40 →
  28. 28.2x + 2y = 30 and 3x + 6y = 72 →
  29. 29.5x + 3y = −6 and 2x + 4y = 20 →
  30. 30.4x − 3y = 27 and 4x + y = 39 →
  31. 31.3x − 2y = −5 and 3x + 4y = 19 →
  32. 32.6x + 3y = −9 and 3x + 6y = −27 →
  33. 33.2x + 3y = 35 and x − 4y = −21 →
  34. 34.5x + 2y = −30 and 2x + 5y = 9 →
  35. 35.6x + 3y = −18 and 2x + 3y = −14 →
  36. 36.2x + 3y = −6 and 3x − 6y = 33 →
  37. 37.4x + 3y = −17 and 3x + 4y = −18 →
  38. 38.x + 3y = 22 and 6x + 5y = 15 →
  39. 39.5x + 4y = 62 and x − y = −2 →
  40. 40.6x + 2y = 20 and 2x + 6y = −36 →

Answer key

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

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