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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 187 · 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. 1.3x + y = 10 and x + 3y = 14 →
  2. 2.x − 6y = 0 and x − y = 5 →
  3. 3.x − 5y = 49 and x − 2y = 25 →
  4. 4.x + 7y = −52 and 7x + y = 20 →
  5. 5.2x + 7y = −7 and 7x + 2y = −47 →
  6. 6.3x + 2y = 26 and 2x + 3y = 24 →
  7. 7.x − 6y = −15 and 5x − 6y = −27 →
  8. 8.x + 5y = −31 and x − y = 11 →
  9. 9.x + 6y = 38 and 6x + 2y = −10 →
  10. 10.3x + y = −21 and 6x − 2y = −18 →
  11. 11.7x + 6y = −22 and 6x + 7y = −17 →
  12. 12.9x + 3y = 3 and 3x + 9y = −15 →
  13. 13.8x + 3y = 46 and 3x + 8y = 31 →
  14. 14.x + 8y = −13 and 8x + y = −41 →
  15. 15.7x + 6y = 86 and 6x + 7y = 83 →
  16. 16.2x + 5y = 29 and 5x + 2y = −1 →
  17. 17.x − 6y = −45 and 5x − 6y = −9 →
  18. 18.3x + 5y = −32 and 5x + 3y = −32 →
  19. 19.2x + y = 17 and 3x − 3y = 21 →
  20. 20.3x − 5y = 32 and 6x − 5y = 44 →
  21. 21.5x + 2y = 4 and 5x + 4y = 18 →
  22. 22.6x + 5y = 41 and 5x + 6y = 47 →
  23. 23.x − 5y = 23 and 5x + 5y = 25 →
  24. 24.5x − 4y = 23 and x − 5y = −8 →
  25. 25.5x + y = −37 and 5x − 4y = −27 →
  26. 26.3x + 5y = −3 and 3x + 2y = 15 →
  27. 27.7x + 5y = −3 and 5x + 7y = −9 →
  28. 28.4x + 4y = 28 and 2x + y = 16 →
  29. 29.4x − 5y = 34 and 5x + 6y = −31 →
  30. 30.5x + 7y = 40 and 7x + 5y = 32 →
  31. 31.2x + y = −13 and 6x + 6y = −30 →
  32. 32.x + 2y = 9 and x + y = 4 →
  33. 33.2x + y = 3 and 3x + 6y = −27 →
  34. 34.7x + 6y = −110 and 6x + 7y = −111 →
  35. 35.4x + 4y = 24 and 2x + 3y = 19 →
  36. 36.x − 4y = 2 and 4x + y = −9 →
  37. 37.3x − 4y = −30 and 3x + 4y = −6 →
  38. 38.x + 2y = 1 and 5x + y = −22 →
  39. 39.3x + 6y = 9 and 6x + 4y = −30 →
  40. 40.x + 4y = 7 and 3x + 2y = 11 →

Answer key

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

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