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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 159 · 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. 1.2x − 2y = −2 and 5x + 2y = 23 →
  2. 2.x + 3y = 16 and 3x + y = 8 →
  3. 3.6x − 6y = 66 and 2x + y = 13 →
  4. 4.3x + 6y = 63 and 6x + 3y = 63 →
  5. 5.9x + y = −36 and x + 9y = −84 →
  6. 6.3x + 6y = 21 and 6x + 3y = 15 →
  7. 7.4x + 2y = 4 and 3x − 6y = 18 →
  8. 8.9x + 8y = −29 and 8x + 9y = −22 →
  9. 9.7x + 6y = −15 and 6x + 7y = −11 →
  10. 10.3x − 4y = −22 and 3x + 6y = −12 →
  11. 11.x − 2y = 0 and x + y = 6 →
  12. 12.2x − y = 20 and x − 5y = 19 →
  13. 13.2x + y = 11 and x + 4y = −5 →
  14. 14.x + 6y = 37 and 4x − 5y = 3 →
  15. 15.x + 8y = 66 and 8x + y = 24 →
  16. 16.9x + 8y = 46 and 8x + 9y = 39 →
  17. 17.4x + y = 8 and 4x − 4y = −12 →
  18. 18.x − 5y = −26 and 3x + 3y = 48 →
  19. 19.x + 4y = −42 and 5x + 2y = −48 →
  20. 20.3x + 7y = −40 and 7x + 3y = 0 →
  21. 21.7x + 6y = 76 and 6x + 7y = 80 →
  22. 22.4x + 2y = 4 and 6x + 2y = −2 →
  23. 23.3x + 4y = 12 and 4x + 3y = 2 →
  24. 24.x + 3y = 33 and 3x − 2y = 11 →
  25. 25.x + 2y = 3 and 5x − 3y = −11 →
  26. 26.5x + 7y = −44 and 7x + 5y = −28 →
  27. 27.3x − 5y = −3 and 2x + y = −15 →
  28. 28.5x + 4y = 49 and 4x + 5y = 50 →
  29. 29.7x + 9y = 144 and 9x + 7y = 144 →
  30. 30.3x + 2y = 20 and 2x + 3y = 25 →
  31. 31.4x + 2y = −6 and 4x − 5y = 1 →
  32. 32.5x + y = 23 and 5x − 6y = 37 →
  33. 33.6x + 6y = 54 and 6x + 5y = 48 →
  34. 34.4x + 2y = −10 and 4x + y = −13 →
  35. 35.4x + 3y = 44 and 3x + 4y = 40 →
  36. 36.3x + 4y = 35 and 4x + 2y = 20 →
  37. 37.4x + 3y = 2 and 5x − 6y = 22 →
  38. 38.5x + 5y = 55 and 6x + y = 26 →
  39. 39.x − y = −4 and x − 4y = −25 →
  40. 40.6x + 3y = 81 and x + y = 18 →

Answer key

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

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