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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 927 · 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 − 4y = 17 and 3x + 3y = 21 →
  2. 2.x − 6y = −8 and 5x − 3y = 14 →
  3. 3.6x − y = 49 and 2x − y = 13 →
  4. 4.3x − 2y = −34 and 3x + 2y = −14 →
  5. 5.7x + 4y = −1 and 4x + 7y = −10 →
  6. 6.3x + 5y = −66 and 2x − 5y = 31 →
  7. 7.9x + y = 14 and x + 9y = 46 →
  8. 8.4x + 9y = −9 and 9x + 4y = −69 →
  9. 9.3x + y = 20 and 2x + 2y = 24 →
  10. 10.x + y = 10 and 2x − 4y = 14 →
  11. 11.2x + y = 3 and x − y = 12 →
  12. 12.5x − y = 42 and 5x − 2y = 49 →
  13. 13.6x + y = −35 and 6x − 4y = −40 →
  14. 14.3x − 2y = 13 and x − 4y = 1 →
  15. 15.4x − 4y = 8 and 3x − 2y = 13 →
  16. 16.5x + 8y = 39 and 8x + 5y = 0 →
  17. 17.x + 6y = 19 and 6x − 4y = −46 →
  18. 18.9x + 2y = −90 and 2x + 9y = −97 →
  19. 19.9x + 4y = 25 and 4x + 9y = −25 →
  20. 20.x + y = 6 and 4x + 6y = 38 →
  21. 21.x + y = −8 and x − y = 2 →
  22. 22.x − 5y = 26 and 6x + 6y = 12 →
  23. 23.3x + 6y = 30 and x + y = 9 →
  24. 24.4x − y = −21 and 4x + 6y = 14 →
  25. 25.2x + 6y = 42 and 6x + 2y = 30 →
  26. 26.x + 5y = 33 and 5x + 5y = 65 →
  27. 27.6x + 2y = −34 and 2x − 4y = −44 →
  28. 28.4x + 6y = −2 and 6x + 4y = 22 →
  29. 29.3x + 7y = −17 and 7x + 3y = −13 →
  30. 30.3x + y = 12 and x + 2y = 9 →
  31. 31.5x − y = 9 and 5x + y = 11 →
  32. 32.8x + 2y = −60 and 2x + 8y = −30 →
  33. 33.5x + 6y = 57 and 5x + y = 22 →
  34. 34.x + 3y = 18 and 3x + y = 22 →
  35. 35.x + 4y = −22 and 6x + 3y = −27 →
  36. 36.3x + y = 3 and 6x − 4y = −30 →
  37. 37.6x + 6y = −30 and 4x − y = −35 →
  38. 38.x + 3y = 20 and 5x − 3y = 10 →
  39. 39.4x + 2y = 30 and 4x + 4y = 44 →
  40. 40.x + 3y = −2 and 3x + 6y = −9 →

Answer key

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

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