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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 81 · 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.x − 3y = 5 and x − 5y = 11 →
  2. 2.5x + 3y = 33 and 3x + 4y = 22 →
  3. 3.5x + 6y = −36 and 2x − 2y = −10 →
  4. 4.5x + 2y = 0 and x + 6y = 28 →
  5. 5.x + 3y = 23 and 2x + 4y = 28 →
  6. 6.5x + 3y = 6 and 3x + 2y = 5 →
  7. 7.2x + 3y = −21 and 5x − y = −27 →
  8. 8.3x + 2y = 22 and 5x − y = 41 →
  9. 9.4x + 2y = 20 and 2x + 5y = 42 →
  10. 10.5x + 3y = 42 and 3x + 5y = 54 →
  11. 11.5x + 7y = 87 and 7x + 5y = 93 →
  12. 12.5x + 7y = −2 and 7x + 5y = 26 →
  13. 13.4x + 8y = 68 and 8x + 4y = 88 →
  14. 14.6x + 4y = −6 and 2x − 4y = 14 →
  15. 15.6x + 4y = −14 and 4x + 6y = −6 →
  16. 16.3x − 3y = −12 and 5x + y = 22 →
  17. 17.4x + 3y = −23 and 5x + 3y = −31 →
  18. 18.x + 5y = −35 and 5x + y = 17 →
  19. 19.7x + 4y = −3 and 4x + 7y = 3 →
  20. 20.3x − y = −26 and 4x − 3y = −38 →
  21. 21.3x + 2y = 9 and 6x + y = 0 →
  22. 22.5x + y = 21 and x + y = 9 →
  23. 23.2x + 5y = 29 and 5x + y = −31 →
  24. 24.5x − y = 38 and 4x − 4y = 24 →
  25. 25.3x + 5y = 9 and 5x + 3y = 31 →
  26. 26.x + 4y = −37 and 3x + y = −12 →
  27. 27.2x − y = −23 and 3x + 2y = −10 →
  28. 28.2x + y = −26 and x + 2y = −25 →
  29. 29.4x + 4y = 56 and 5x − 6y = −29 →
  30. 30.6x − 6y = −12 and 3x − 6y = −18 →
  31. 31.4x + y = 26 and 3x − 5y = 8 →
  32. 32.5x + 3y = −18 and 6x − 6y = −60 →
  33. 33.x + 6y = −39 and 5x + 4y = −65 →
  34. 34.x − y = −2 and x + 2y = −20 →
  35. 35.9x + y = 48 and x + 9y = −48 →
  36. 36.x − 5y = −9 and 3x + y = −11 →
  37. 37.2x + 6y = 0 and 6x + 2y = −16 →
  38. 38.6x − 4y = 32 and 2x − 5y = 29 →
  39. 39.5x + 6y = 81 and 3x − 3y = 9 →
  40. 40.3x + 6y = 72 and 4x − 6y = −30 →

Answer key

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

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