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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 157 · 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. 1.3x + 4y = 17 and 4x − 4y = 4 →
  2. 2.4x + 8y = 44 and 8x + 4y = 16 →
  3. 3.4x + y = 25 and 6x + 2y = 40 →
  4. 4.3x − 6y = −21 and 2x + y = −4 →
  5. 5.x + 2y = 17 and 6x − 4y = −26 →
  6. 6.5x + 6y = −7 and 3x − 6y = 15 →
  7. 7.6x + 7y = −10 and 7x + 6y = −3 →
  8. 8.3x + 9y = 93 and 9x + 3y = 87 →
  9. 9.3x + 2y = 25 and 2x + 3y = 30 →
  10. 10.5x + 6y = 31 and 6x + 5y = 35 →
  11. 11.x + 2y = −11 and 5x + 4y = −7 →
  12. 12.x + 2y = 8 and x − 6y = −8 →
  13. 13.5x − 4y = −11 and 6x − y = −17 →
  14. 14.6x − 4y = 46 and 2x − y = 15 →
  15. 15.2x − 2y = 2 and 5x − 2y = 14 →
  16. 16.3x + 3y = −36 and 2x + 5y = −33 →
  17. 17.x + 3y = 33 and 2x + 3y = 42 →
  18. 18.2x + 2y = −14 and 5x + 6y = −33 →
  19. 19.2x + 6y = 20 and 5x + y = −34 →
  20. 20.2x − y = −5 and 5x + 4y = 46 →
  21. 21.4x + y = −20 and 4x − 2y = −8 →
  22. 22.2x + 3y = −2 and 4x + y = −14 →
  23. 23.7x + 2y = 36 and 2x + 7y = 36 →
  24. 24.6x + 4y = 22 and 4x + 6y = 18 →
  25. 25.x + 5y = 27 and 5x + 4y = 9 →
  26. 26.x − 6y = 3 and x + y = 10 →
  27. 27.2x − 5y = 14 and 2x + 3y = −2 →
  28. 28.x + 3y = 10 and 3x + y = 6 →
  29. 29.2x + 4y = −6 and 6x − y = −44 →
  30. 30.6x − 4y = 78 and 6x + 3y = 36 →
  31. 31.x + 2y = 26 and 5x − 5y = −5 →
  32. 32.x + 3y = 20 and 5x + 6y = 64 →
  33. 33.7x + 6y = 45 and 6x + 7y = 46 →
  34. 34.2x − 5y = −1 and 6x + 2y = 14 →
  35. 35.6x + 4y = −42 and 2x − 2y = 6 →
  36. 36.8x + 5y = −28 and 5x + 8y = −37 →
  37. 37.x + 2y = 10 and 5x + 3y = 22 →
  38. 38.2x + 6y = 54 and 4x + 6y = 60 →
  39. 39.7x + 9y = 117 and 9x + 7y = 123 →
  40. 40.x + 7y = 41 and 7x + y = 47 →

Answer key

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

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