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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 995 · 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. 1.4x + 6y = 90 and 6x + 4y = 90 →
  2. 2.4x + 3y = −3 and 3x + 6y = 24 →
  3. 3.9x + y = −60 and x + 9y = 20 →
  4. 4.3x + 4y = −6 and 4x + 3y = 6 →
  5. 5.6x + 2y = 6 and 2x + y = 1 →
  6. 6.9x + 8y = −120 and 8x + 9y = −118 →
  7. 7.3x + 8y = −67 and 8x + 3y = −87 →
  8. 8.3x + 8y = −4 and 8x + 3y = 26 →
  9. 9.x + 8y = 70 and 8x + y = −7 →
  10. 10.x − 6y = 49 and 3x + 4y = −29 →
  11. 11.7x + 2y = 77 and 2x + 7y = 67 →
  12. 12.7x + 2y = −11 and 2x + 7y = −61 →
  13. 13.7x + 6y = 80 and 6x + 7y = 76 →
  14. 14.5x + y = 22 and 6x + 2y = 20 →
  15. 15.2x − 6y = 0 and 4x + 2y = 28 →
  16. 16.2x + y = 3 and 3x + 5y = 29 →
  17. 17.4x − 6y = −8 and 5x + 6y = 71 →
  18. 18.2x + 6y = 38 and 2x + 3y = 26 →
  19. 19.3x − 2y = 24 and 2x − 2y = 18 →
  20. 20.x + 5y = 14 and 6x − 4y = −52 →
  21. 21.5x + 6y = −34 and 6x + 5y = −43 →
  22. 22.3x + 2y = 29 and 2x + 5y = 34 →
  23. 23.9x + 2y = 42 and 2x + 9y = −42 →
  24. 24.2x + y = −8 and 4x − 2y = −32 →
  25. 25.x + 2y = −9 and 3x + 5y = −21 →
  26. 26.x + 9y = 44 and 9x + y = −4 →
  27. 27.x + 6y = −12 and 2x + 4y = −16 →
  28. 28.2x + 2y = 28 and 3x − 5y = −22 →
  29. 29.3x − 4y = −33 and x − 6y = −53 →
  30. 30.x + 2y = 18 and 6x + 4y = 44 →
  31. 31.x + y = −3 and x + 2y = 3 →
  32. 32.4x + 4y = 28 and 4x − 6y = −32 →
  33. 33.5x − 2y = 38 and 3x − y = 23 →
  34. 34.9x + 4y = 64 and 4x + 9y = 14 →
  35. 35.x + y = 3 and 2x + 6y = −10 →
  36. 36.6x + 8y = 4 and 8x + 6y = 24 →
  37. 37.4x − 2y = 26 and 5x + 2y = 46 →
  38. 38.5x + 2y = 44 and x + 6y = 48 →
  39. 39.3x + 3y = 21 and x + 5y = 19 →
  40. 40.3x + 5y = −54 and 2x − 4y = 30 →

Answer key

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

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