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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 171 · 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.x + 7y = 43 and 7x + y = 13 →
  2. 2.4x − 4y = −12 and x − 4y = −27 →
  3. 3.2x − 6y = −48 and 2x − 3y = −27 →
  4. 4.3x + y = 5 and 3x − 4y = 25 →
  5. 5.4x + 3y = 33 and 4x + 5y = 39 →
  6. 6.9x + 5y = −98 and 5x + 9y = −98 →
  7. 7.3x + 3y = −39 and 2x + 6y = −62 →
  8. 8.6x − 6y = 36 and 5x − 2y = 33 →
  9. 9.2x − 3y = −38 and x + y = 1 →
  10. 10.5x + 3y = 51 and x + 2y = 20 →
  11. 11.8x + 7y = 61 and 7x + 8y = 59 →
  12. 12.x − y = 3 and x − 6y = −22 →
  13. 13.5x + 3y = 59 and x − 5y = −33 →
  14. 14.5x + 5y = −25 and 5x − y = −31 →
  15. 15.8x + 7y = −12 and 7x + 8y = −18 →
  16. 16.8x + 2y = 10 and 2x + 8y = −20 →
  17. 17.6x + 3y = −15 and 3x + 6y = −3 →
  18. 18.3x + 4y = −7 and 4x + 4y = −12 →
  19. 19.6x + 7y = −77 and 7x + 6y = −79 →
  20. 20.6x + 2y = 34 and 2x + 6y = 54 →
  21. 21.6x + 3y = 18 and 3x + 6y = 27 →
  22. 22.6x + 2y = 22 and 5x − 2y = 11 →
  23. 23.9x + 3y = −6 and 3x + 9y = 54 →
  24. 24.5x − 6y = −3 and 5x + y = 18 →
  25. 25.3x + 2y = 15 and 5x + 6y = 33 →
  26. 26.2x + 4y = 28 and 3x − 2y = −6 →
  27. 27.5x − y = 11 and 2x + 4y = 22 →
  28. 28.3x + 2y = 23 and 2x + 4y = 26 →
  29. 29.x − 6y = 8 and 6x + 5y = −34 →
  30. 30.x + 3y = 0 and 3x + y = 16 →
  31. 31.x + 6y = −18 and 6x + y = 32 →
  32. 32.3x − y = −23 and 6x + 6y = −6 →
  33. 33.2x + 2y = −2 and x − 3y = −13 →
  34. 34.6x + 5y = 38 and 3x − 3y = −3 →
  35. 35.8x + y = 56 and x + 8y = −56 →
  36. 36.4x − 5y = 23 and 5x + y = 36 →
  37. 37.6x − 5y = 31 and 2x − 6y = 6 →
  38. 38.5x + 5y = −20 and 5x − 2y = −34 →
  39. 39.4x − 6y = 28 and x + y = −3 →
  40. 40.6x + 2y = 0 and x − 2y = 14 →

Answer key

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

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