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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 211 · 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 − 3y = −7 and 6x − 3y = 33 →
  2. 2.5x + y = −34 and x + 5y = 22 →
  3. 3.2x + y = 13 and x + 2y = 17 →
  4. 4.2x − 5y = −6 and 6x − 4y = 26 →
  5. 5.2x + 2y = −2 and 3x + y = −7 →
  6. 6.3x + y = 26 and 6x − 4y = 4 →
  7. 7.5x − 4y = −6 and 4x + 2y = −36 →
  8. 8.6x + 3y = 18 and 5x + 6y = 1 →
  9. 9.2x + 5y = 49 and 5x + 2y = 28 →
  10. 10.4x + 5y = −3 and x − 5y = 18 →
  11. 11.3x + 6y = 27 and 4x + y = 8 →
  12. 12.x + 7y = 29 and 7x + y = 11 →
  13. 13.2x + 2y = −6 and 3x − 3y = −39 →
  14. 14.5x + 2y = 23 and 2x + 5y = 26 →
  15. 15.6x + y = −21 and 2x − 4y = −20 →
  16. 16.x + 7y = 47 and 7x + y = 41 →
  17. 17.2x + 7y = 54 and 7x + 2y = 54 →
  18. 18.2x − y = −12 and 6x − 6y = −30 →
  19. 19.4x − 2y = 20 and 4x − 5y = 14 →
  20. 20.4x + 7y = 55 and 7x + 4y = 55 →
  21. 21.6x + 2y = 20 and 2x + 6y = 28 →
  22. 22.5x + y = −45 and x + 5y = −33 →
  23. 23.x + 9y = −27 and 9x + y = −83 →
  24. 24.2x − y = 7 and 2x + 4y = 22 →
  25. 25.x + 5y = 32 and 4x + 3y = 9 →
  26. 26.x + 6y = 25 and 2x + y = 17 →
  27. 27.6x − 4y = −14 and 5x − 2y = −17 →
  28. 28.5x + 6y = 51 and 2x − 2y = 16 →
  29. 29.5x − 4y = 5 and 3x + 3y = −24 →
  30. 30.x + 2y = 17 and 2x − y = 9 →
  31. 31.4x − 6y = 24 and 2x + 6y = −6 →
  32. 32.9x + 6y = −21 and 6x + 9y = −24 →
  33. 33.5x + 2y = 33 and 4x + 3y = 32 →
  34. 34.5x + 9y = −19 and 9x + 5y = −23 →
  35. 35.8x + y = 67 and x + 8y = 32 →
  36. 36.x − 5y = −35 and 3x + 4y = 9 →
  37. 37.x + 3y = 14 and 3x + y = 10 →
  38. 38.x − 5y = −36 and x − 3y = −22 →
  39. 39.4x + 3y = 57 and 3x + 4y = 55 →
  40. 40.8x + 7y = 67 and 7x + 8y = 68 →

Answer key

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

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