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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 869 · 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. 1.7x + 5y = 34 and 5x + 7y = 14 →
  2. 2.2x + 5y = 18 and 4x + 5y = 26 →
  3. 3.x − 2y = −4 and 5x + 6y = 76 →
  4. 4.2x − 2y = 0 and 5x + y = 24 →
  5. 5.7x + 9y = 51 and 9x + 7y = 29 →
  6. 6.x + 2y = −9 and x + 5y = −30 →
  7. 7.3x + 2y = −9 and x + 4y = −33 →
  8. 8.x − 5y = −11 and 4x + 6y = 8 →
  9. 9.4x + 4y = 8 and 3x − 3y = −42 →
  10. 10.4x + 6y = −48 and 6x + 4y = −52 →
  11. 11.5x + 3y = 28 and x − y = −4 →
  12. 12.5x + 3y = −9 and 4x − 3y = −18 →
  13. 13.x − 6y = −21 and 3x + 2y = 17 →
  14. 14.2x + 6y = −12 and 3x + 3y = 0 →
  15. 15.4x + y = 25 and x + 3y = −13 →
  16. 16.6x − y = 45 and 5x + 6y = 17 →
  17. 17.3x + 4y = 16 and 6x + 5y = 11 →
  18. 18.4x + 2y = 30 and 2x − 6y = −6 →
  19. 19.9x + 8y = −57 and 8x + 9y = −45 →
  20. 20.6x + 5y = −26 and 5x + 6y = −29 →
  21. 21.x + 2y = 4 and 2x + y = −4 →
  22. 22.x + 4y = 34 and x − 4y = −22 →
  23. 23.3x + 7y = −47 and 7x + 3y = −3 →
  24. 24.6x + 5y = 14 and 2x − 3y = 14 →
  25. 25.3x + 5y = 1 and 6x + y = 38 →
  26. 26.2x + 6y = 46 and x − 2y = −17 →
  27. 27.x + 5y = −14 and 4x − 6y = −4 →
  28. 28.6x + y = 19 and 3x − 3y = 6 →
  29. 29.4x + y = −5 and x − 6y = 5 →
  30. 30.7x + y = −59 and x + 7y = −29 →
  31. 31.4x − y = −21 and x + 6y = 26 →
  32. 32.6x + 4y = 22 and x − 6y = −3 →
  33. 33.2x + y = 11 and x + 2y = 13 →
  34. 34.6x + 4y = 50 and 5x − 3y = 29 →
  35. 35.8x + 4y = −48 and 4x + 8y = −12 →
  36. 36.5x + 4y = 31 and 3x − 2y = −21 →
  37. 37.6x + 6y = 54 and 5x − y = 15 →
  38. 38.3x − y = 31 and x + 5y = −11 →
  39. 39.4x + 5y = −27 and 4x + y = −31 →
  40. 40.7x + 3y = 17 and 3x + 7y = −27 →

Answer key

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

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