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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 14 · 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. 1.9x + 3y = −9 and 3x + 9y = 21 →
  2. 2.3x − y = 17 and 2x − 6y = 6 →
  3. 3.9x + 7y = 40 and 7x + 9y = 24 →
  4. 4.3x + 6y = −48 and 6x + 3y = −42 →
  5. 5.3x − 6y = −30 and 4x + 5y = −1 →
  6. 6.8x + 4y = 72 and 4x + 8y = 60 →
  7. 7.3x − 3y = −15 and 3x + 5y = −47 →
  8. 8.x − 2y = −21 and 5x + y = −28 →
  9. 9.x + 5y = −2 and 6x + 4y = −38 →
  10. 10.3x + 6y = 63 and 6x + 3y = 63 →
  11. 11.6x − 3y = −27 and 4x − y = −19 →
  12. 12.7x + y = 18 and x + 7y = 30 →
  13. 13.2x + 2y = 20 and 6x − 4y = −10 →
  14. 14.5x + 9y = 35 and 9x + 5y = 7 →
  15. 15.4x + y = 12 and 5x − 2y = 41 →
  16. 16.6x + 4y = 64 and 4x + y = 31 →
  17. 17.3x + y = 12 and 5x + y = 14 →
  18. 18.3x + 4y = 16 and x + 2y = 4 →
  19. 19.x + 6y = −49 and x + y = −14 →
  20. 20.2x − 2y = −14 and 3x − y = −15 →
  21. 21.6x − 2y = 24 and 4x + 3y = 42 →
  22. 22.2x + y = 4 and 6x − 2y = 22 →
  23. 23.6x + 2y = 2 and 6x + 3y = 6 →
  24. 24.x + 2y = 2 and 3x + 4y = 10 →
  25. 25.x + 2y = 11 and 2x + y = 1 →
  26. 26.x + 8y = 67 and 8x + y = 32 →
  27. 27.2x + 5y = 22 and x + 3y = 12 →
  28. 28.x + 2y = 2 and 6x − 5y = 46 →
  29. 29.8x + 5y = 70 and 5x + 8y = 73 →
  30. 30.5x − 3y = −9 and 2x − 2y = −10 →
  31. 31.x + 6y = 52 and 3x + 2y = 12 →
  32. 32.x − 3y = −2 and 5x + 2y = 7 →
  33. 33.5x + 7y = −94 and 7x + 5y = −98 →
  34. 34.5x + 5y = 25 and 4x − 2y = 2 →
  35. 35.3x + 5y = 28 and 5x + 3y = 4 →
  36. 36.7x + 8y = 29 and 8x + 7y = 16 →
  37. 37.4x − 4y = 12 and 2x − 3y = 3 →
  38. 38.4x + 3y = 43 and 4x + 5y = 61 →
  39. 39.5x − 4y = 14 and 4x + 2y = 32 →
  40. 40.x − y = 15 and 2x + 4y = −24 →

Answer key

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

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