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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 417 · 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 + 2y = 16 and 3x + 2y = 28 →
  2. 2.9x + y = 88 and x + 9y = 72 →
  3. 3.x + 6y = 21 and 2x − 3y = −18 →
  4. 4.6x − 5y = −11 and x + 2y = 18 →
  5. 5.x + 4y = 19 and 4x + y = −29 →
  6. 6.5x + y = −4 and 6x − 3y = −30 →
  7. 7.7x + 2y = 33 and 2x + 7y = −42 →
  8. 8.3x + 9y = −33 and 9x + 3y = −27 →
  9. 9.5x + 4y = −28 and 4x + 5y = −17 →
  10. 10.6x + 3y = 33 and 3x − 5y = −42 →
  11. 11.2x − 5y = 58 and 4x + 6y = −12 →
  12. 12.x + 9y = 63 and 9x + y = −73 →
  13. 13.8x + 9y = −111 and 9x + 8y = −110 →
  14. 14.2x + 2y = 36 and 2x + 4y = 54 →
  15. 15.3x + 6y = 57 and 5x + y = 23 →
  16. 16.x + 4y = −27 and 4x − 3y = −13 →
  17. 17.3x − y = 20 and 2x − y = 12 →
  18. 18.2x − y = 13 and x + 2y = −16 →
  19. 19.6x + 4y = 32 and 3x + 5y = 13 →
  20. 20.2x + 5y = 19 and 5x + 2y = 37 →
  21. 21.6x − y = 60 and 4x − 6y = 72 →
  22. 22.3x + 6y = 60 and 6x − y = 42 →
  23. 23.8x + 4y = 28 and 4x + 8y = −16 →
  24. 24.4x + 2y = −46 and 5x − y = −26 →
  25. 25.6x − 3y = 12 and 2x + 5y = 16 →
  26. 26.2x + 6y = 48 and 2x + 2y = 20 →
  27. 27.8x + 2y = 34 and 2x + 8y = −44 →
  28. 28.4x + 5y = 57 and 5x + 4y = 51 →
  29. 29.2x + 4y = 22 and 4x + 2y = 26 →
  30. 30.2x + y = 13 and 2x − 3y = −15 →
  31. 31.8x + 7y = 97 and 7x + 8y = 98 →
  32. 32.6x − 5y = 5 and x + 6y = −47 →
  33. 33.x + y = −2 and 2x − 5y = −53 →
  34. 34.5x − 5y = −25 and 3x + 5y = 57 →
  35. 35.3x + 2y = 16 and 2x + 3y = 4 →
  36. 36.6x − 2y = 34 and x + y = 15 →
  37. 37.6x + y = 5 and x + 2y = −12 →
  38. 38.6x + y = −8 and 3x + 2y = 2 →
  39. 39.3x + 6y = 48 and 2x − 5y = −4 →
  40. 40.2x + y = 11 and 4x + 3y = 17 →

Answer key

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

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