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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 116 · 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 = 42 and 3x + 5y = 23 →
  2. 2.2x + 6y = 60 and 2x − y = −3 →
  3. 3.x + 7y = 23 and 7x + y = 17 →
  4. 4.6x + 6y = 78 and 4x + 3y = 48 →
  5. 5.2x − y = −1 and x + 5y = 27 →
  6. 6.x − 6y = −16 and x + 5y = 28 →
  7. 7.5x − 4y = −51 and 3x + 6y = 45 →
  8. 8.x + 4y = −19 and 4x + y = 14 →
  9. 9.x + 6y = −10 and 4x + 5y = 17 →
  10. 10.4x − 6y = 10 and x + y = 10 →
  11. 11.6x − 5y = −64 and 3x − 4y = −44 →
  12. 12.2x + y = 14 and x + 2y = 10 →
  13. 13.5x + 5y = 35 and x − y = −11 →
  14. 14.6x − 2y = 66 and 4x − 4y = 68 →
  15. 15.8x + 5y = 60 and 5x + 8y = 57 →
  16. 16.x + y = −7 and 4x + 5y = −36 →
  17. 17.6x − y = 41 and 5x + y = 47 →
  18. 18.3x + y = 23 and x + y = 5 →
  19. 19.6x + 5y = −33 and 5x + 6y = −22 →
  20. 20.x + y = 14 and 5x + 6y = 78 →
  21. 21.x − 2y = 22 and 2x − 2y = 28 →
  22. 22.4x + 2y = 20 and 4x + 4y = 36 →
  23. 23.x + 6y = 31 and 2x − 4y = −18 →
  24. 24.3x + y = −3 and 4x + 6y = 24 →
  25. 25.9x + 6y = −27 and 6x + 9y = −3 →
  26. 26.3x − 4y = −26 and 5x − y = 2 →
  27. 27.x + 5y = 19 and 4x + 3y = 8 →
  28. 28.4x + 3y = 11 and 5x − y = 28 →
  29. 29.6x + 4y = 30 and 4x + 5y = 34 →
  30. 30.3x + 6y = 33 and 6x + 3y = 21 →
  31. 31.4x + 6y = −90 and 4x − 6y = 18 →
  32. 32.x − 5y = 12 and 2x − 5y = 14 →
  33. 33.6x − 5y = 39 and 6x + 5y = 69 →
  34. 34.6x + 6y = 60 and 6x − 5y = −39 →
  35. 35.4x + 4y = −12 and 4x − 2y = 42 →
  36. 36.9x + 7y = 137 and 7x + 9y = 135 →
  37. 37.3x + 5y = −37 and x + 2y = −15 →
  38. 38.3x + 5y = 5 and 5x + y = −21 →
  39. 39.8x + 4y = −52 and 4x + 8y = 4 →
  40. 40.6x + 2y = 66 and x + 4y = 33 →

Answer key

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

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