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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 105 · 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. 1.2x + 6y = −40 and 6x − 2y = 40 →
  2. 2.2x + 6y = −24 and 6x + 2y = 8 →
  3. 3.x + 2y = 10 and x + y = 7 →
  4. 4.6x + 2y = 48 and 2x − 6y = −24 →
  5. 5.6x + y = −33 and x + 6y = 47 →
  6. 6.x + 2y = −5 and 2x + y = −1 →
  7. 7.6x + 2y = −32 and 3x + 4y = −10 →
  8. 8.6x + 8y = 32 and 8x + 6y = 38 →
  9. 9.x + 3y = 34 and 6x + 3y = 69 →
  10. 10.3x + 5y = −24 and 5x − 5y = 80 →
  11. 11.6x + 5y = 49 and 4x + 5y = 41 →
  12. 12.4x + 6y = −52 and 4x − 2y = −4 →
  13. 13.x − 5y = −36 and x − 4y = −28 →
  14. 14.8x + y = 43 and x + 8y = −34 →
  15. 15.3x + y = −29 and 2x − 4y = 18 →
  16. 16.4x + y = 5 and 6x + 5y = 11 →
  17. 17.6x + 7y = 90 and 7x + 6y = 92 →
  18. 18.4x + 8y = 16 and 8x + 4y = 20 →
  19. 19.5x + 5y = 0 and 6x + y = 25 →
  20. 20.x + 3y = 17 and 4x + 3y = −4 →
  21. 21.3x + 5y = 37 and 2x + 6y = 46 →
  22. 22.2x + 4y = −34 and 2x − 2y = 2 →
  23. 23.2x + 3y = 22 and 3x − y = 22 →
  24. 24.4x + y = 6 and x + 5y = −27 →
  25. 25.5x − 6y = −52 and 6x + 2y = −44 →
  26. 26.6x + y = −11 and 5x − 4y = 15 →
  27. 27.8x + 5y = 36 and 5x + 8y = 42 →
  28. 28.6x + 2y = −30 and 4x + 2y = −14 →
  29. 29.3x + 3y = 30 and 4x − 4y = 8 →
  30. 30.2x + 2y = 2 and 3x + 2y = 5 →
  31. 31.3x − 2y = 4 and 4x + 3y = 45 →
  32. 32.5x + 4y = 18 and 6x + 2y = 16 →
  33. 33.x + 5y = −22 and 6x + 4y = −28 →
  34. 34.5x + 9y = −57 and 9x + 5y = −13 →
  35. 35.3x − y = −8 and 2x − 3y = −17 →
  36. 36.x + 6y = 44 and 6x + y = 54 →
  37. 37.x + 3y = −10 and 6x − 4y = 50 →
  38. 38.2x + y = −21 and 6x + y = −45 →
  39. 39.4x − 2y = 34 and 2x − 4y = 38 →
  40. 40.6x + 5y = 65 and 3x − 6y = −27 →

Answer key

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

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