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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 102 · 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 + 3y = 39 and 6x − 4y = 32 →
  2. 2.5x + 4y = 16 and 6x + 4y = 24 →
  3. 3.2x + 2y = −12 and x + 6y = −31 →
  4. 4.4x + 9y = 29 and 9x + 4y = −16 →
  5. 5.x + y = 8 and 6x − 2y = 24 →
  6. 6.2x + 4y = 14 and 4x + 2y = 16 →
  7. 7.2x + 5y = 39 and x − 2y = −3 →
  8. 8.4x − 6y = 10 and 6x + 4y = 28 →
  9. 9.9x + 7y = 50 and 7x + 9y = 46 →
  10. 10.6x + 5y = 57 and 6x − y = 39 →
  11. 11.x + y = −2 and 6x + y = −27 →
  12. 12.x + 3y = 7 and 3x + y = 5 →
  13. 13.6x + y = 21 and 4x + 6y = 62 →
  14. 14.5x + y = 48 and 2x + 2y = 32 →
  15. 15.2x − 6y = −18 and 2x + 6y = 54 →
  16. 16.x + 5y = 28 and 4x − 6y = −18 →
  17. 17.2x − 6y = 20 and 2x + 5y = −2 →
  18. 18.2x − 3y = −8 and 5x + 3y = 1 →
  19. 19.4x + 7y = 36 and 7x + 4y = 30 →
  20. 20.x + 5y = 18 and 5x + y = 42 →
  21. 21.2x + 4y = 28 and 4x + 2y = 32 →
  22. 22.4x + 2y = 34 and x + y = 13 →
  23. 23.9x + 8y = −126 and 8x + 9y = −129 →
  24. 24.x + 5y = −16 and 5x + y = 40 →
  25. 25.2x + 4y = 42 and 4x + 2y = 42 →
  26. 26.3x − y = 5 and 3x + 2y = −19 →
  27. 27.2x + 8y = −30 and 8x + 2y = 30 →
  28. 28.7x + 8y = 40 and 8x + 7y = 50 →
  29. 29.6x + 3y = 66 and 4x − 2y = 12 →
  30. 30.9x + 5y = −14 and 5x + 9y = 42 →
  31. 31.5x + 2y = −43 and 5x − 3y = −48 →
  32. 32.4x + y = −6 and x + 4y = 21 →
  33. 33.x + 2y = −9 and 2x + y = −9 →
  34. 34.2x − 5y = 19 and 4x − 3y = 17 →
  35. 35.3x + y = −22 and x + 3y = −26 →
  36. 36.x + 2y = 21 and 6x − 6y = 18 →
  37. 37.3x + 8y = −22 and 8x + 3y = 33 →
  38. 38.x + 8y = −35 and 8x + y = −28 →
  39. 39.2x + 4y = −10 and 6x + 4y = 26 →
  40. 40.2x + y = 3 and 5x + 4y = 0 →

Answer key

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

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