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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 897 · 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 + 2y = 30 and 2x + 8y = 0 →
  2. 2.2x + 3y = 15 and x − 6y = −60 →
  3. 3.6x + 2y = −54 and 5x − 4y = −28 →
  4. 4.2x + 5y = −22 and 5x + 2y = −13 →
  5. 5.4x − 6y = 8 and 5x + 5y = 35 →
  6. 6.x − 2y = 1 and 5x − 6y = 17 →
  7. 7.3x − 4y = −34 and 6x + y = −5 →
  8. 8.4x − 5y = 13 and x − y = 4 →
  9. 9.x − 2y = −12 and 6x + 2y = 26 →
  10. 10.9x + 3y = 72 and 3x + 9y = 96 →
  11. 11.3x − 6y = −60 and 2x − 6y = −58 →
  12. 12.7x + 3y = −25 and 3x + 7y = −45 →
  13. 13.x + 4y = −32 and 6x − 2y = −10 →
  14. 14.2x + 2y = 24 and 5x − y = 30 →
  15. 15.4x + 9y = 38 and 9x + 4y = −12 →
  16. 16.4x − y = 1 and 3x + 4y = −23 →
  17. 17.2x + y = 9 and x + 2y = −9 →
  18. 18.x + 2y = 2 and 4x − 4y = −40 →
  19. 19.2x + y = 10 and 4x + 5y = 26 →
  20. 20.3x + 2y = 37 and 3x − 3y = 12 →
  21. 21.4x + 7y = 56 and 7x + 4y = 65 →
  22. 22.8x + 3y = 30 and 3x + 8y = 25 →
  23. 23.7x + y = 31 and x + 7y = −23 →
  24. 24.4x + 3y = −1 and 5x − y = 32 →
  25. 25.x + y = 15 and 4x + 2y = 44 →
  26. 26.6x + y = 8 and 3x − 5y = −7 →
  27. 27.9x + 4y = −21 and 4x + 9y = −31 →
  28. 28.x + y = −9 and 3x + 2y = −26 →
  29. 29.6x + 2y = −44 and x − y = −10 →
  30. 30.2x + 4y = −22 and 4x − 4y = 64 →
  31. 31.3x − 6y = 12 and 4x + 3y = 27 →
  32. 32.5x + 5y = 50 and 3x + 4y = 39 →
  33. 33.5x + 5y = 80 and 4x + 5y = 71 →
  34. 34.x − 2y = −8 and 4x − 3y = 3 →
  35. 35.9x + 4y = 93 and 4x + 9y = 63 →
  36. 36.7x + 4y = −36 and 4x + 7y = −30 →
  37. 37.6x + 8y = −20 and 8x + 6y = −36 →
  38. 38.3x + 4y = −5 and 6x + 3y = −15 →
  39. 39.3x − 6y = 6 and 2x + 6y = 34 →
  40. 40.4x + y = 17 and x + 4y = 8 →

Answer key

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

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