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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 128 · 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 + 9y = 21 and 9x + 6y = −6 →
  2. 2.3x − 3y = −9 and 5x + y = 27 →
  3. 3.4x + 2y = 14 and 2x + 4y = −20 →
  4. 4.3x − y = 14 and 5x + 4y = 29 →
  5. 5.5x + 4y = 13 and 4x + 5y = 14 →
  6. 6.4x + y = 31 and 2x − 4y = 2 →
  7. 7.2x + 4y = −14 and 2x + 2y = 2 →
  8. 8.3x − 5y = −57 and 6x − y = −33 →
  9. 9.5x + 2y = 46 and 6x − 3y = 12 →
  10. 10.2x + 7y = 13 and 7x + 2y = 23 →
  11. 11.x + 6y = −10 and 6x + y = −25 →
  12. 12.5x + 4y = 68 and 5x + 2y = 54 →
  13. 13.x + 4y = 16 and x + y = −2 →
  14. 14.3x + 6y = 24 and x + 5y = 29 →
  15. 15.4x − 5y = 76 and x + 3y = −15 →
  16. 16.3x + y = −24 and 4x − y = −39 →
  17. 17.3x − 5y = 54 and 5x + y = 34 →
  18. 18.5x − 5y = 0 and 5x − 3y = −4 →
  19. 19.9x + 5y = −28 and 5x + 9y = 28 →
  20. 20.5x + 2y = 26 and 2x + y = 12 →
  21. 21.4x + 6y = −52 and 6x − y = −38 →
  22. 22.6x + 8y = 50 and 8x + 6y = 48 →
  23. 23.5x − 3y = −54 and 2x − 6y = −36 →
  24. 24.x + 4y = −12 and 5x − 3y = −37 →
  25. 25.6x + 7y = −44 and 7x + 6y = −34 →
  26. 26.5x − 3y = −42 and 6x + 4y = −58 →
  27. 27.2x + 3y = −17 and 6x − 2y = −40 →
  28. 28.5x − 5y = −85 and 5x + 4y = −4 →
  29. 29.5x + 3y = 24 and 2x + 5y = −17 →
  30. 30.x − 3y = 12 and 2x + 5y = 13 →
  31. 31.x + 4y = 43 and 6x − 6y = −12 →
  32. 32.x − 4y = 0 and 4x + 2y = 36 →
  33. 33.4x + 5y = 21 and 5x + 4y = 24 →
  34. 34.4x + 9y = −55 and 9x + 4y = −10 →
  35. 35.2x − y = −7 and 6x + 2y = 24 →
  36. 36.5x + 3y = 11 and 6x + 4y = 14 →
  37. 37.2x − 4y = 38 and x − 6y = 51 →
  38. 38.3x + y = −14 and x + 3y = −26 →
  39. 39.5x + 6y = −4 and 6x + 5y = −18 →
  40. 40.2x + 8y = −14 and 8x + 2y = 34 →

Answer key

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

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