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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 571 · 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 + 8y = 23 and 8x + 7y = 37 →
  2. 2.2x + y = 15 and 3x + 3y = 24 →
  3. 3.7x + 3y = 40 and 3x + 7y = 0 →
  4. 4.6x + 4y = −18 and 6x − 3y = −81 →
  5. 5.2x + y = 0 and 2x − 2y = −24 →
  6. 6.x + 4y = 9 and 3x + 5y = 20 →
  7. 7.3x + 7y = 58 and 7x + 3y = 42 →
  8. 8.2x + 8y = 34 and 8x + 2y = 76 →
  9. 9.6x + 3y = 51 and x + y = 9 →
  10. 10.2x + 6y = 50 and 6x + 2y = 22 →
  11. 11.x + 5y = 14 and 5x + y = 46 →
  12. 12.5x − 5y = −20 and 3x + 4y = 9 →
  13. 13.4x − 5y = −37 and 5x + 6y = −34 →
  14. 14.x − 3y = −10 and 3x + 6y = 15 →
  15. 15.x + y = −12 and x + 4y = −27 →
  16. 16.5x + y = 12 and 5x + 6y = 22 →
  17. 17.3x + y = 6 and x + 3y = −14 →
  18. 18.6x − y = 50 and 3x + 2y = 20 →
  19. 19.3x − 5y = −50 and x + 6y = 37 →
  20. 20.3x + 6y = −27 and 6x + 2y = −34 →
  21. 21.7x + 5y = −39 and 5x + 7y = −21 →
  22. 22.4x + 5y = −17 and 2x + y = −1 →
  23. 23.3x + 8y = 29 and 8x + 3y = 59 →
  24. 24.x − 3y = −4 and 6x + 5y = 22 →
  25. 25.2x + 5y = 53 and 5x + 2y = 59 →
  26. 26.4x + 7y = 23 and 7x + 4y = 32 →
  27. 27.6x + 4y = 14 and 4x + 6y = −14 →
  28. 28.x + 4y = −1 and 6x + y = 40 →
  29. 29.4x + 2y = −52 and x + 6y = −57 →
  30. 30.3x − y = −12 and 6x + 5y = 39 →
  31. 31.x − 3y = 19 and 3x − 6y = 30 →
  32. 32.2x + 3y = −25 and 5x − 5y = 50 →
  33. 33.2x + 2y = −22 and 2x − 2y = 14 →
  34. 34.5x − 6y = −6 and x − 2y = −6 →
  35. 35.3x + 3y = 12 and x + 5y = 0 →
  36. 36.2x − y = −7 and x − 3y = −26 →
  37. 37.6x + 2y = 36 and 4x − 5y = −33 →
  38. 38.4x + 2y = 38 and 6x − y = 53 →
  39. 39.7x + 5y = 39 and 5x + 7y = 45 →
  40. 40.6x + 4y = −12 and 2x + y = −5 →

Answer key

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

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