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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 195 · 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 + 3y = 3 and 4x − 4y = 56 →
  2. 2.2x − y = −11 and 5x − 3y = −28 →
  3. 3.5x + 3y = 51 and 3x + 5y = 53 →
  4. 4.6x − 3y = 3 and 3x + 2y = 5 →
  5. 5.2x + 5y = 25 and 5x + 2y = 31 →
  6. 6.6x + 3y = 63 and 2x + 2y = 24 →
  7. 7.3x + 3y = 33 and x + 2y = 16 →
  8. 8.7x + 8y = −32 and 8x + 7y = −43 →
  9. 9.2x + 4y = −24 and 4x + 2y = 0 →
  10. 10.4x − 6y = 62 and x + y = −2 →
  11. 11.2x − 5y = 41 and 3x + y = 2 →
  12. 12.6x + y = −4 and x + 6y = 11 →
  13. 13.2x − 6y = 14 and x + y = −5 →
  14. 14.6x + 5y = −47 and 2x + 2y = −16 →
  15. 15.3x + 8y = 65 and 8x + 3y = 45 →
  16. 16.2x + 5y = −49 and 6x − 2y = −28 →
  17. 17.6x − 5y = 25 and 5x + 3y = 28 →
  18. 18.3x − 3y = −3 and x + y = 5 →
  19. 19.7x + 2y = −37 and 2x + 7y = −17 →
  20. 20.4x + 5y = 27 and 5x + 4y = 27 →
  21. 21.6x + 5y = −7 and 4x + 2y = −6 →
  22. 22.2x − 6y = 22 and 2x + 6y = 10 →
  23. 23.2x − 3y = −29 and 6x + y = −37 →
  24. 24.5x + 8y = 77 and 8x + 5y = 53 →
  25. 25.3x + 5y = −12 and x + 5y = −24 →
  26. 26.7x + y = 21 and x + 7y = 51 →
  27. 27.5x − 3y = −10 and x + 2y = 11 →
  28. 28.2x + y = −13 and x + y = −8 →
  29. 29.4x + 2y = 34 and 2x + 4y = 20 →
  30. 30.5x + 5y = 25 and 5x + 3y = 31 →
  31. 31.x + 2y = 20 and 2x + y = 13 →
  32. 32.6x + y = −38 and x + 6y = −53 →
  33. 33.4x − 3y = 5 and x + 6y = 8 →
  34. 34.4x + 5y = 27 and 5x + 4y = 18 →
  35. 35.6x + 5y = 7 and 3x + 6y = 0 →
  36. 36.5x − 6y = 41 and 2x + 5y = 9 →
  37. 37.6x + 2y = −30 and 2x + 6y = −42 →
  38. 38.3x − 3y = −18 and 5x + 6y = 47 →
  39. 39.2x − y = −12 and 6x + 6y = 36 →
  40. 40.6x + y = 51 and 5x + 3y = 62 →

Answer key

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

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