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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 220 · 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. 1.4x + 6y = 26 and 6x + 4y = 24 →
  2. 2.4x − 4y = 8 and 3x + 4y = 55 →
  3. 3.3x + 6y = −3 and 4x + 2y = 26 →
  4. 4.7x + 5y = 62 and 5x + 7y = 58 →
  5. 5.6x − 4y = −32 and 2x − 2y = −14 →
  6. 6.8x + 5y = 87 and 5x + 8y = 69 →
  7. 7.2x + 4y = −34 and x + 5y = −44 →
  8. 8.2x − 2y = 4 and 4x − y = 17 →
  9. 9.4x − 4y = −32 and x − 3y = −14 →
  10. 10.x + 2y = 18 and 2x + y = 21 →
  11. 11.7x + 4y = 43 and 4x + 7y = 34 →
  12. 12.x + 3y = −4 and 6x + 6y = −12 →
  13. 13.5x + 2y = 39 and 2x + 5y = 24 →
  14. 14.2x + 6y = −22 and 6x + 2y = −2 →
  15. 15.x − 3y = −13 and 2x + 5y = 18 →
  16. 16.6x + 6y = 36 and x + 2y = 10 →
  17. 17.6x + y = 31 and 5x − 5y = −15 →
  18. 18.4x + y = −27 and x + 4y = −3 →
  19. 19.x + 2y = −9 and 2x + y = −3 →
  20. 20.6x − 2y = 22 and 5x − 4y = 16 →
  21. 21.x + 3y = 4 and 3x − 3y = 0 →
  22. 22.4x + 3y = 48 and 6x + 5y = 76 →
  23. 23.x + 6y = −26 and x − 6y = 10 →
  24. 24.x + 3y = 30 and 4x + 6y = 78 →
  25. 25.4x + 3y = 23 and 3x + 4y = 26 →
  26. 26.5x + 8y = −27 and 8x + 5y = −51 →
  27. 27.5x + 3y = 33 and 2x − 2y = −6 →
  28. 28.9x + 5y = −57 and 5x + 9y = −13 →
  29. 29.2x + y = 23 and 5x − 5y = 5 →
  30. 30.9x + 7y = 68 and 7x + 9y = 60 →
  31. 31.x + 9y = 22 and 9x + y = −42 →
  32. 32.5x − 3y = 17 and 6x + 3y = 60 →
  33. 33.2x + 3y = 20 and 5x + 4y = 29 →
  34. 34.8x + 6y = 10 and 6x + 8y = 4 →
  35. 35.9x + 2y = −23 and 2x + 9y = 12 →
  36. 36.6x + y = −33 and 5x + 2y = −38 →
  37. 37.4x + 3y = −17 and 3x + 4y = −25 →
  38. 38.8x + 3y = 11 and 3x + 8y = 11 →
  39. 39.8x + 7y = −20 and 7x + 8y = −25 →
  40. 40.6x + 2y = −10 and x + 3y = 9 →

Answer key

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

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