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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 25 · 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. 1.3x + 6y = 12 and 2x + 2y = 6 →
  2. 2.x − 3y = −23 and x + 3y = 31 →
  3. 3.5x + 4y = −67 and 4x − 4y = 4 →
  4. 4.6x − y = −30 and 4x + 5y = 14 →
  5. 5.3x + 5y = −34 and 5x + 3y = −14 →
  6. 6.6x + 7y = 32 and 7x + 6y = 20 →
  7. 7.7x + 6y = 20 and 6x + 7y = 32 →
  8. 8.2x + 6y = −28 and 6x + 2y = 12 →
  9. 9.2x + 6y = −6 and 5x − 4y = 42 →
  10. 10.2x − y = 21 and 3x − 4y = 54 →
  11. 11.3x − 6y = 69 and 5x + y = 38 →
  12. 12.5x + 6y = 64 and 2x − y = −5 →
  13. 13.5x + 3y = 37 and x + 6y = 2 →
  14. 14.3x + 6y = −54 and x + 3y = −26 →
  15. 15.3x + 8y = 55 and 8x + 3y = 55 →
  16. 16.3x + 2y = 2 and 2x + 3y = 13 →
  17. 17.6x + 3y = −36 and 3x + 6y = −36 →
  18. 18.6x + 2y = −16 and 2x − 6y = −32 →
  19. 19.2x + 4y = 10 and x − 6y = −35 →
  20. 20.4x + y = −31 and x + 4y = −4 →
  21. 21.3x + 5y = −7 and 3x + 6y = −12 →
  22. 22.8x + 5y = 102 and 5x + 8y = 93 →
  23. 23.9x + 8y = 4 and 8x + 9y = 13 →
  24. 24.2x + 8y = 44 and 8x + 2y = 26 →
  25. 25.3x + 4y = −13 and 2x + 3y = −11 →
  26. 26.3x + 2y = −19 and 2x + 3y = −11 →
  27. 27.3x − 6y = −9 and 6x − 2y = −38 →
  28. 28.5x + 3y = 8 and 3x + 2y = 3 →
  29. 29.6x − 2y = 4 and 6x + y = 7 →
  30. 30.x + 6y = −10 and 6x + y = 10 →
  31. 31.x + 2y = 7 and x − y = −14 →
  32. 32.5x + 4y = 7 and 3x + 6y = −3 →
  33. 33.9x + y = 85 and x + 9y = 45 →
  34. 34.3x + y = −26 and 6x + 4y = −50 →
  35. 35.3x + 4y = 26 and 4x + 3y = 16 →
  36. 36.6x + 5y = −42 and 6x + 6y = −48 →
  37. 37.8x + y = 67 and x + 8y = 32 →
  38. 38.2x + 4y = 34 and x + y = 11 →
  39. 39.2x + 4y = −38 and 4x + 3y = −31 →
  40. 40.4x + 2y = −34 and 3x + 3y = −33 →

Answer key

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

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