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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 611 · 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 + 2y = −10 and 5x + y = −33 →
  2. 2.x + 3y = 30 and 6x + y = 27 →
  3. 3.6x − 6y = 0 and 2x − 6y = −16 →
  4. 4.6x + 2y = 4 and 2x + 6y = −4 →
  5. 5.2x + 5y = −22 and 6x + 2y = 38 →
  6. 6.2x + 8y = −22 and 8x + 2y = −58 →
  7. 7.4x + 3y = −11 and 3x + 4y = −3 →
  8. 8.2x + 3y = −23 and 6x + 2y = −34 →
  9. 9.4x + 2y = 6 and 3x − 6y = 27 →
  10. 10.3x + 6y = 63 and 6x + 3y = 63 →
  11. 11.5x + 6y = −21 and 2x + 2y = −6 →
  12. 12.4x + 2y = 12 and 6x − 4y = 4 →
  13. 13.5x + y = 52 and 2x − 3y = −3 →
  14. 14.5x + 2y = 34 and 2x + 5y = 43 →
  15. 15.8x + 5y = 54 and 5x + 8y = 63 →
  16. 16.x − y = −7 and 6x + 2y = 30 →
  17. 17.4x − 3y = −19 and 3x + 3y = −9 →
  18. 18.7x + 6y = 117 and 6x + 7y = 117 →
  19. 19.4x + 2y = −30 and 5x − 2y = −24 →
  20. 20.2x − 3y = −11 and 6x − 6y = −24 →
  21. 21.x + 2y = −2 and 4x + 3y = −23 →
  22. 22.3x + 6y = 30 and 2x + 2y = 12 →
  23. 23.x + 5y = 36 and 2x + 2y = 24 →
  24. 24.2x + 6y = 8 and 4x + 6y = 10 →
  25. 25.3x + 4y = −15 and 6x + 2y = 24 →
  26. 26.6x − 6y = −102 and 2x + 5y = 22 →
  27. 27.6x + 3y = 15 and 3x + 6y = −33 →
  28. 28.6x + 4y = −34 and 4x − 6y = −66 →
  29. 29.6x + 5y = 2 and x − 4y = 10 →
  30. 30.3x − 5y = −5 and 6x − y = 26 →
  31. 31.x + 4y = 33 and 6x + 3y = 30 →
  32. 32.6x + 5y = −69 and x + 6y = −27 →
  33. 33.x − 2y = −5 and 2x + y = 25 →
  34. 34.3x − 5y = −18 and 4x + 2y = 54 →
  35. 35.5x − y = −11 and 2x − 6y = −38 →
  36. 36.5x + 4y = 18 and 4x − 6y = −4 →
  37. 37.4x + 5y = −13 and 5x − 4y = −6 →
  38. 38.2x + 8y = 40 and 8x + 2y = 40 →
  39. 39.3x + 5y = −46 and 5x + 3y = −50 →
  40. 40.4x + 3y = −21 and 3x + 4y = −7 →

Answer key

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

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