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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 255 · 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 + y = 10 and x + y = 4 →
  2. 2.3x − y = −11 and 2x + 3y = 11 →
  3. 3.x + 2y = 9 and x + 4y = 11 →
  4. 4.x − 3y = −4 and x − 6y = −10 →
  5. 5.3x − 3y = −9 and 5x + 4y = 3 →
  6. 6.3x − 3y = −3 and 4x + 4y = −12 →
  7. 7.x − 5y = −27 and 2x + 6y = 10 →
  8. 8.2x − 3y = 27 and 3x − 5y = 43 →
  9. 9.3x + 3y = −9 and x + 4y = −6 →
  10. 10.6x − 6y = −54 and 3x + 2y = −12 →
  11. 11.x + 2y = −14 and 2x + y = −1 →
  12. 12.6x + 4y = 30 and 6x − y = 15 →
  13. 13.2x + 7y = 46 and 7x + 2y = 71 →
  14. 14.4x − 2y = −30 and 3x + 5y = 36 →
  15. 15.2x + 3y = 3 and 3x + 2y = 12 →
  16. 16.4x − 2y = −22 and 6x − 4y = −38 →
  17. 17.3x + 4y = −18 and 4x + 3y = −10 →
  18. 18.8x + y = 35 and x + 8y = −35 →
  19. 19.x − y = 9 and 3x − 6y = 51 →
  20. 20.x − 3y = −25 and x + y = −1 →
  21. 21.3x + 4y = −23 and 3x − 3y = −30 →
  22. 22.6x + y = 1 and 6x + 2y = −4 →
  23. 23.2x + 5y = 24 and 5x + 2y = 18 →
  24. 24.5x + 6y = −14 and 6x + 5y = 3 →
  25. 25.6x − y = 1 and 5x + 3y = −26 →
  26. 26.2x + y = −9 and x + 2y = 3 →
  27. 27.4x − 4y = 36 and x − 2y = 13 →
  28. 28.5x + 4y = −2 and 3x − 6y = −60 →
  29. 29.6x + 7y = 51 and 7x + 6y = 40 →
  30. 30.5x + 4y = 5 and 4x + 5y = 13 →
  31. 31.4x − 6y = 68 and 5x + 2y = 9 →
  32. 32.9x + 3y = 30 and 3x + 9y = 18 →
  33. 33.3x + 7y = 57 and 7x + 3y = 13 →
  34. 34.9x + 3y = 33 and 3x + 9y = 51 →
  35. 35.x + 2y = 16 and x + 5y = 28 →
  36. 36.x − 4y = 10 and 6x + 4y = 32 →
  37. 37.5x + 6y = −47 and 6x + 5y = −41 →
  38. 38.9x + 2y = 73 and 2x + 9y = 59 →
  39. 39.2x − y = 1 and 3x − 6y = −30 →
  40. 40.6x + 3y = 39 and 3x − 4y = 3 →

Answer key

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

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