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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 59 · 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. 1.2x + y = −11 and x + 2y = 5 →
  2. 2.5x + y = 18 and x + 5y = −6 →
  3. 3.x + 3y = −4 and x − 3y = 20 →
  4. 4.4x + 6y = 52 and 4x + 2y = 28 →
  5. 5.6x − y = −39 and 5x − 4y = −61 →
  6. 6.x − 5y = −42 and 4x + y = 0 →
  7. 7.7x + 2y = 20 and 2x + 7y = −20 →
  8. 8.4x − y = 25 and 4x − 4y = 4 →
  9. 9.6x + 8y = −78 and 8x + 6y = −90 →
  10. 10.x + 9y = 86 and 9x + y = 54 →
  11. 11.3x + y = −8 and 5x − 3y = −46 →
  12. 12.5x + y = 7 and 2x + 5y = 12 →
  13. 13.x + y = −3 and 3x + 4y = −16 →
  14. 14.x + 3y = 14 and 4x − y = −35 →
  15. 15.x + 4y = 26 and x − 2y = −10 →
  16. 16.x + 4y = 20 and x + 2y = 8 →
  17. 17.4x + 7y = 8 and 7x + 4y = −19 →
  18. 18.5x + 4y = 67 and 6x + 3y = 66 →
  19. 19.2x − 5y = −19 and 6x + 2y = 62 →
  20. 20.5x + y = −12 and x + 5y = 12 →
  21. 21.2x + 4y = −4 and 4x + 2y = 22 →
  22. 22.4x + 9y = −5 and 9x + 4y = −60 →
  23. 23.4x + 8y = −4 and 8x + 4y = 52 →
  24. 24.6x − 5y = 31 and 2x + 2y = 14 →
  25. 25.5x + 6y = 37 and 2x + 3y = 19 →
  26. 26.7x + 9y = 5 and 9x + 7y = −21 →
  27. 27.x + 9y = 79 and 9x + y = −9 →
  28. 28.5x + 2y = −39 and 6x + 4y = −42 →
  29. 29.4x + 5y = 6 and 3x + 2y = −6 →
  30. 30.3x + 5y = 42 and 4x + y = 5 →
  31. 31.3x + 2y = 29 and 5x + 5y = 55 →
  32. 32.2x − y = −6 and 3x + y = 1 →
  33. 33.9x + 5y = −92 and 5x + 9y = −76 →
  34. 34.5x + 2y = 43 and 2x + 5y = 13 →
  35. 35.3x + 7y = 30 and 7x + 3y = 30 →
  36. 36.3x + 8y = 42 and 8x + 3y = 2 →
  37. 37.5x − y = −42 and x + 3y = −2 →
  38. 38.5x + y = 8 and 3x + y = 6 →
  39. 39.5x + 3y = −13 and 3x + 5y = 21 →
  40. 40.5x + y = −4 and x + 5y = 4 →

Answer key

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

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