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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 905 · 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 + y = 9 and 2x + 6y = 38 →
  2. 2.3x − 3y = 21 and x − 5y = 3 →
  3. 3.x + 5y = 25 and 5x + y = −19 →
  4. 4.2x − y = −27 and x − 2y = −27 →
  5. 5.3x + 4y = −7 and x + 3y = −14 →
  6. 6.2x − y = 0 and 2x − 4y = −12 →
  7. 7.2x + 5y = −21 and 5x − 4y = 30 →
  8. 8.x − 5y = 44 and 4x + 4y = −16 →
  9. 9.6x + 6y = 66 and 3x + 2y = 26 →
  10. 10.6x + 3y = 27 and 5x + 6y = 26 →
  11. 11.6x − 6y = 24 and 3x + 6y = −51 →
  12. 12.9x + 4y = 36 and 4x + 9y = −49 →
  13. 13.7x + y = 31 and x + 7y = −23 →
  14. 14.6x − y = 57 and 4x + 4y = 24 →
  15. 15.4x − 3y = 13 and 4x + y = 33 →
  16. 16.9x + 2y = −56 and 2x + 9y = 56 →
  17. 17.x + y = 11 and 6x − 2y = 50 →
  18. 18.4x − 2y = −22 and 3x − y = −14 →
  19. 19.x + 6y = 63 and 4x + 4y = 72 →
  20. 20.4x + 6y = 70 and 4x + 5y = 61 →
  21. 21.4x + 8y = 28 and 8x + 4y = −16 →
  22. 22.2x + 4y = 38 and 2x + 5y = 46 →
  23. 23.7x + 2y = 70 and 2x + 7y = 65 →
  24. 24.9x + 7y = 12 and 7x + 9y = 20 →
  25. 25.2x − 5y = 8 and x + y = 11 →
  26. 26.2x + 7y = −23 and 7x + 2y = 32 →
  27. 27.4x + 6y = −52 and 6x + 4y = −48 →
  28. 28.2x + 6y = 16 and 2x + y = 11 →
  29. 29.6x − 6y = −36 and 6x + 6y = −60 →
  30. 30.6x + 2y = 0 and 2x + 2y = −4 →
  31. 31.3x + 6y = 6 and 6x + 3y = −33 →
  32. 32.4x − y = 5 and 5x + 6y = 57 →
  33. 33.9x + 5y = 32 and 5x + 9y = −32 →
  34. 34.x − 2y = 2 and 4x + 4y = −40 →
  35. 35.3x + 2y = 23 and 2x + 3y = 12 →
  36. 36.4x + 5y = 25 and 6x − 6y = −84 →
  37. 37.x − 5y = −29 and 3x + 2y = 15 →
  38. 38.5x + y = 22 and 4x + 6y = 28 →
  39. 39.4x + 5y = 48 and x − y = 3 →
  40. 40.x + 4y = 14 and 4x − 2y = 2 →

Answer key

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

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