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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 192 · 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 = 6 and 2x + 5y = 9 →
  2. 2.5x + 2y = 31 and 6x − 5y = 15 →
  3. 3.5x − 3y = 69 and 2x − 3y = 42 →
  4. 4.2x + 6y = 12 and x + y = 4 →
  5. 5.8x + 7y = −47 and 7x + 8y = −58 →
  6. 6.5x + 3y = 4 and 4x + 2y = 0 →
  7. 7.3x + y = −35 and x + 3y = −33 →
  8. 8.2x + y = −6 and 3x + 6y = 0 →
  9. 9.8x + 5y = −37 and 5x + 8y = −28 →
  10. 10.5x + 4y = −34 and 4x + y = −25 →
  11. 11.5x + 8y = 37 and 8x + 5y = −11 →
  12. 12.8x + y = 49 and x + 8y = 77 →
  13. 13.2x + 4y = −6 and 4x + 2y = 18 →
  14. 14.6x + 7y = 59 and 7x + 6y = 58 →
  15. 15.4x + 3y = 11 and 3x + 4y = 3 →
  16. 16.3x + 2y = −2 and 2x − 3y = 16 →
  17. 17.4x + 2y = 44 and 5x − 4y = 3 →
  18. 18.6x + 5y = 18 and x − 6y = −38 →
  19. 19.4x + 2y = 16 and x + 3y = 19 →
  20. 20.8x + 2y = 48 and 2x + 8y = −48 →
  21. 21.x + 3y = 6 and 3x + y = −6 →
  22. 22.3x + 5y = 16 and x + 6y = 14 →
  23. 23.x + 2y = −7 and 2x + y = −5 →
  24. 24.4x + y = 21 and 6x + 6y = 54 →
  25. 25.7x + 8y = −17 and 8x + 7y = −28 →
  26. 26.x + 6y = −28 and 6x + y = 7 →
  27. 27.6x + y = −50 and x + 6y = 15 →
  28. 28.6x + y = 25 and x + 3y = 7 →
  29. 29.4x + y = −10 and 5x + 3y = −2 →
  30. 30.3x + 4y = 60 and 5x + 4y = 76 →
  31. 31.x + 6y = 36 and 2x + 6y = 42 →
  32. 32.x + 4y = 17 and 5x + 3y = 51 →
  33. 33.2x + 3y = −19 and 3x + 2y = −6 →
  34. 34.7x + 8y = 85 and 8x + 7y = 80 →
  35. 35.5x + 6y = −33 and 6x + 3y = −48 →
  36. 36.5x + 6y = −16 and 6x − 4y = −64 →
  37. 37.x + 3y = 11 and x + 2y = 10 →
  38. 38.4x + 3y = −29 and 6x + y = −33 →
  39. 39.4x + 2y = −8 and 6x + 4y = −14 →
  40. 40.5x + 7y = 71 and 7x + 5y = 61 →

Answer key

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

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