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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 445 · 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. 1.6x + 5y = 3 and 5x + 6y = −14 →
  2. 2.6x − 3y = −9 and 2x + 6y = 32 →
  3. 3.2x + 5y = −4 and 3x + 3y = 3 →
  4. 4.8x + 4y = −12 and 4x + 8y = 36 →
  5. 5.6x − 5y = 99 and 5x + 6y = −9 →
  6. 6.3x + 8y = 66 and 8x + 3y = 66 →
  7. 7.x − 4y = 40 and x + 3y = −23 →
  8. 8.2x + 6y = −30 and 3x + 5y = −17 →
  9. 9.3x + 5y = 29 and 5x + 3y = 43 →
  10. 10.6x + 4y = 38 and 5x − 2y = 21 →
  11. 11.7x + 5y = 54 and 5x + 7y = 42 →
  12. 12.2x + 4y = −2 and 5x − 5y = −35 →
  13. 13.2x + 5y = 34 and 5x + 2y = 1 →
  14. 14.6x + y = −54 and x + 6y = −44 →
  15. 15.x + 5y = 17 and x − 2y = −11 →
  16. 16.8x + 3y = 9 and 3x + 8y = −31 →
  17. 17.2x − 3y = 0 and 6x − 5y = 8 →
  18. 18.3x + y = −11 and 5x + 6y = 12 →
  19. 19.5x + 3y = 29 and 5x − 6y = 47 →
  20. 20.3x + 4y = −14 and 4x + 3y = −21 →
  21. 21.6x + 9y = −30 and 9x + 6y = −60 →
  22. 22.6x + 4y = 22 and 4x + 6y = −2 →
  23. 23.4x + 6y = −2 and 6x + 4y = −18 →
  24. 24.4x − 4y = −60 and 3x + 4y = 4 →
  25. 25.4x − 4y = −20 and 3x + y = 9 →
  26. 26.3x + 9y = −78 and 9x + 3y = −90 →
  27. 27.4x + 9y = 78 and 9x + 4y = 78 →
  28. 28.3x − y = −19 and 6x − 5y = −50 →
  29. 29.2x + 6y = −8 and 4x − 2y = 26 →
  30. 30.4x + 5y = −30 and 6x + 4y = −38 →
  31. 31.4x + 6y = 72 and 6x + 4y = 78 →
  32. 32.6x + 4y = 76 and x − 3y = −13 →
  33. 33.6x + 3y = −12 and x + 6y = −13 →
  34. 34.5x + 6y = 14 and 2x + 3y = 8 →
  35. 35.x + 6y = 45 and 6x + y = 25 →
  36. 36.7x + 2y = 52 and 2x + 7y = 47 →
  37. 37.x − 5y = −49 and 5x − y = −53 →
  38. 38.3x + 2y = −7 and 5x − 5y = −45 →
  39. 39.8x + 3y = 56 and 3x + 8y = 76 →
  40. 40.9x + 2y = 41 and 2x + 9y = −8 →

Answer key

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

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