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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 576 · 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 + 6y = 60 and 4x + y = 22 →
  2. 2.7x + 2y = −47 and 2x + 7y = −7 →
  3. 3.4x − 6y = 30 and 2x + y = 3 →
  4. 4.x + 5y = 40 and 2x + y = 17 →
  5. 5.3x + 5y = 44 and 2x − 2y = −8 →
  6. 6.2x + 6y = 18 and 2x + 2y = 10 →
  7. 7.9x + 2y = 84 and 2x + 9y = 70 →
  8. 8.3x + 5y = −28 and x − 5y = 24 →
  9. 9.4x + 5y = 32 and x − 2y = −5 →
  10. 10.3x + 3y = −12 and 3x − 5y = 52 →
  11. 11.x + 6y = 36 and 6x + y = 41 →
  12. 12.2x − 4y = −16 and x − 4y = −24 →
  13. 13.6x + 5y = −16 and 5x + 6y = −6 →
  14. 14.9x + y = −62 and x + 9y = 2 →
  15. 15.2x + 4y = −32 and 6x + y = −52 →
  16. 16.2x + 4y = 2 and 5x + 3y = −9 →
  17. 17.x + 5y = −41 and 2x − 3y = 22 →
  18. 18.3x + y = 1 and 2x − 3y = −14 →
  19. 19.5x + y = −19 and x + 5y = 1 →
  20. 20.6x + y = 13 and 6x + 5y = 41 →
  21. 21.x − 3y = −24 and 4x + 6y = 12 →
  22. 22.4x + 6y = −10 and 5x + 3y = 1 →
  23. 23.2x + 6y = −8 and x + 4y = −7 →
  24. 24.6x − 2y = −56 and 2x + 5y = 4 →
  25. 25.x + 6y = 54 and x + 2y = 22 →
  26. 26.3x + 5y = −7 and 2x − 5y = −13 →
  27. 27.2x + y = 17 and 6x + 2y = 42 →
  28. 28.2x + 4y = 10 and x − y = −1 →
  29. 29.5x + 8y = 56 and 8x + 5y = 74 →
  30. 30.2x + 2y = −2 and 4x + 5y = 4 →
  31. 31.3x − 6y = −27 and 4x + 4y = 24 →
  32. 32.6x + y = −33 and 2x + 5y = 31 →
  33. 33.9x + 3y = 96 and 3x + 9y = 72 →
  34. 34.3x + y = 14 and 2x + 5y = 18 →
  35. 35.4x − y = 34 and 2x + 3y = 10 →
  36. 36.x + 9y = −71 and 9x + y = 1 →
  37. 37.4x + y = 25 and 3x − 3y = 45 →
  38. 38.x + 5y = −24 and 6x + 2y = −60 →
  39. 39.6x + 4y = 22 and 3x + y = 16 →
  40. 40.6x + 5y = −4 and 5x + 6y = −7 →

Answer key

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

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