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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 103 · 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. 1.8x + 7y = −36 and 7x + 8y = −39 →
  2. 2.7x + 5y = 58 and 5x + 7y = 38 →
  3. 3.5x + 7y = 59 and 7x + 5y = 73 →
  4. 4.2x + 6y = 2 and 2x − 2y = −22 →
  5. 5.5x − 2y = 24 and 2x − 2y = 0 →
  6. 6.3x − 3y = −42 and 4x + 4y = 8 →
  7. 7.6x + y = 38 and 3x − 5y = −25 →
  8. 8.4x + y = 21 and x + 4y = −6 →
  9. 9.5x + 2y = 5 and 2x + 5y = 23 →
  10. 10.3x − 4y = 10 and 2x − 3y = 7 →
  11. 11.2x + 6y = −48 and 6x + 2y = −64 →
  12. 12.3x + 8y = 59 and 8x + 3y = 84 →
  13. 13.4x + 4y = 24 and 4x − 4y = 40 →
  14. 14.6x + 2y = 26 and 2x + 6y = 14 →
  15. 15.4x + 4y = 36 and 6x − 5y = −34 →
  16. 16.6x + 3y = 48 and 2x + 5y = 32 →
  17. 17.6x − 5y = 11 and x − 4y = −14 →
  18. 18.2x + 4y = 18 and 2x + y = 6 →
  19. 19.7x + y = −30 and x + 7y = −18 →
  20. 20.x + 4y = 17 and 3x + y = 29 →
  21. 21.x + y = 11 and 4x − y = −1 →
  22. 22.x − 3y = 6 and 2x + 3y = −24 →
  23. 23.2x + 2y = 26 and 5x + 4y = 61 →
  24. 24.4x − 3y = −1 and 6x + y = 37 →
  25. 25.6x − 5y = −75 and 2x + 5y = 35 →
  26. 26.3x + 2y = 11 and 2x + 3y = 14 →
  27. 27.x + 8y = 55 and 8x + y = −1 →
  28. 28.9x + 7y = 112 and 7x + 9y = 112 →
  29. 29.3x + 5y = 31 and 2x + 2y = 10 →
  30. 30.5x + 9y = −25 and 9x + 5y = 11 →
  31. 31.3x + 2y = −25 and 2x + 3y = −15 →
  32. 32.x − 2y = 12 and 2x − y = 9 →
  33. 33.9x + 7y = −44 and 7x + 9y = −20 →
  34. 34.4x + 3y = 33 and 5x − 3y = −6 →
  35. 35.7x + 5y = 59 and 5x + 7y = 49 →
  36. 36.3x + 3y = 30 and x + 4y = 16 →
  37. 37.x − 4y = 43 and 2x + y = 5 →
  38. 38.x + 3y = −17 and 6x + 3y = −12 →
  39. 39.6x + 4y = 16 and 6x + 2y = 14 →
  40. 40.3x − 2y = −42 and x + 6y = 46 →

Answer key

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

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