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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 35 · 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. 1.5x + 6y = 17 and 6x + 5y = 16 →
  2. 2.4x + 5y = −11 and x + 4y = −11 →
  3. 3.8x + 3y = 36 and 3x + 8y = 41 →
  4. 4.4x + 3y = 52 and 4x + 6y = 76 →
  5. 5.6x + 3y = −9 and 3x + 5y = 6 →
  6. 6.x + 9y = 16 and 9x + y = 64 →
  7. 7.2x + 6y = 10 and 6x + 2y = −2 →
  8. 8.4x + 5y = 12 and 6x + 6y = 12 →
  9. 9.x + 9y = 65 and 9x + y = 25 →
  10. 10.2x − 3y = −5 and 4x − 4y = −8 →
  11. 11.4x + 5y = 77 and 5x + 4y = 76 →
  12. 12.x + 5y = 7 and x + 4y = 6 →
  13. 13.8x + 6y = −8 and 6x + 8y = 8 →
  14. 14.5x + 2y = 29 and x − 6y = 57 →
  15. 15.x + 3y = −17 and 3x + y = −3 →
  16. 16.2x + y = −5 and x + 2y = −1 →
  17. 17.8x + 4y = 52 and 4x + 8y = 20 →
  18. 18.3x + 4y = 9 and x − 4y = −29 →
  19. 19.x − y = 0 and 3x − y = 8 →
  20. 20.2x + 4y = −10 and 4x + 2y = 16 →
  21. 21.x − 3y = 28 and 2x − 5y = 47 →
  22. 22.6x + 5y = −2 and 2x − y = 10 →
  23. 23.6x + 2y = 38 and 2x + 6y = −14 →
  24. 24.x + 4y = 35 and 2x − 2y = −20 →
  25. 25.2x + 2y = 14 and 5x + 6y = 33 →
  26. 26.5x − 4y = 0 and 6x − 5y = −1 →
  27. 27.6x + 6y = −6 and 3x − y = 5 →
  28. 28.6x + 3y = 72 and 2x + 6y = 54 →
  29. 29.2x − y = 23 and 4x + 3y = 21 →
  30. 30.2x + y = 7 and 6x − 5y = −3 →
  31. 31.2x − y = 3 and 4x − 6y = 10 →
  32. 32.9x + 5y = −7 and 5x + 9y = −35 →
  33. 33.6x − 4y = 64 and 4x + 4y = 16 →
  34. 34.6x + y = 57 and x + 6y = 62 →
  35. 35.2x + 5y = 34 and 5x + 2y = 1 →
  36. 36.3x + 9y = 63 and 9x + 3y = −3 →
  37. 37.x + 9y = 76 and 9x + y = 44 →
  38. 38.4x + 5y = 46 and 3x + 2y = 31 →
  39. 39.8x + 7y = 26 and 7x + 8y = 19 →
  40. 40.3x + y = 12 and 5x + 6y = 33 →

Answer key

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

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