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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 261 · 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 + 2y = −12 and 6x + y = −31 →
  2. 2.4x + 4y = 12 and 3x + 5y = 5 →
  3. 3.x + 4y = 32 and 4x + y = 38 →
  4. 4.6x + 5y = 66 and 5x + 6y = 66 →
  5. 5.5x + 4y = 39 and 4x + y = 29 →
  6. 6.x + 5y = −1 and 5x + 2y = 41 →
  7. 7.6x − 5y = −33 and 5x + y = 19 →
  8. 8.3x + 8y = −69 and 8x + 3y = −19 →
  9. 9.x + 3y = 2 and 3x + y = 22 →
  10. 10.6x − y = 21 and 3x − 3y = 18 →
  11. 11.5x + 6y = 41 and 5x + 2y = 37 →
  12. 12.x + 2y = 10 and 6x + 4y = −12 →
  13. 13.6x + 3y = 3 and 3x + 6y = 24 →
  14. 14.x + 5y = 19 and 5x + 6y = 38 →
  15. 15.3x − 4y = −12 and x + 4y = 44 →
  16. 16.6x − 5y = 7 and x + 5y = 7 →
  17. 17.2x + 4y = 18 and 4x + 3y = −4 →
  18. 18.x − 6y = −55 and 6x − 2y = −24 →
  19. 19.3x + 2y = −7 and 4x − 5y = −17 →
  20. 20.2x + 5y = 9 and x + 4y = 12 →
  21. 21.3x + 5y = −33 and 3x + 6y = −39 →
  22. 22.6x + 8y = 88 and 8x + 6y = 94 →
  23. 23.6x − y = 26 and 2x + 6y = 34 →
  24. 24.4x + 4y = 24 and 3x + 2y = 15 →
  25. 25.5x + 9y = −27 and 9x + 5y = −71 →
  26. 26.3x − 3y = 6 and 5x + 6y = 21 →
  27. 27.4x − 5y = 2 and 2x − 2y = 2 →
  28. 28.4x − 2y = 46 and 6x + y = 41 →
  29. 29.3x − y = 20 and x − 2y = −5 →
  30. 30.3x − 6y = −42 and 4x − 5y = −47 →
  31. 31.8x + 9y = 65 and 9x + 8y = 71 →
  32. 32.2x + 4y = 10 and x + 6y = 1 →
  33. 33.4x + 6y = −2 and x + 3y = 4 →
  34. 34.4x + 8y = −20 and 8x + 4y = −64 →
  35. 35.4x − y = 13 and 4x + 3y = 9 →
  36. 36.9x + 2y = 71 and 2x + 9y = 50 →
  37. 37.9x + 3y = 81 and 3x + 9y = 75 →
  38. 38.4x + 5y = −4 and 4x + y = −20 →
  39. 39.5x + 3y = 36 and 4x − 6y = 12 →
  40. 40.4x + 2y = 50 and 2x + 4y = 46 →

Answer key

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

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