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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 228 · 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 − 2y = 18 and 6x + 4y = 28 →
  2. 2.3x + y = 15 and x + 3y = 21 →
  3. 3.5x + y = −10 and x + 5y = −26 →
  4. 4.6x + 4y = −14 and 3x − 3y = −42 →
  5. 5.6x + 2y = −6 and 2x − 2y = −10 →
  6. 6.3x − 3y = −27 and 6x + 2y = −30 →
  7. 7.5x + 9y = −51 and 9x + 5y = −47 →
  8. 8.3x − y = −15 and x + 5y = 43 →
  9. 9.8x + y = 46 and x + 8y = 53 →
  10. 10.6x + 5y = 27 and 2x − 2y = −2 →
  11. 11.x + 4y = 34 and 4x + y = 16 →
  12. 12.4x − 6y = −90 and 3x − 4y = −63 →
  13. 13.4x + 2y = −44 and x − y = −2 →
  14. 14.4x + 4y = −24 and 4x + 5y = −33 →
  15. 15.2x + 3y = 20 and 2x − 5y = 4 →
  16. 16.3x + 3y = 24 and 3x + 6y = 39 →
  17. 17.3x − 6y = 6 and 4x + 4y = 20 →
  18. 18.x + 5y = 35 and 3x + 4y = 39 →
  19. 19.5x + 4y = −37 and 4x + 5y = −44 →
  20. 20.8x + 7y = −127 and 7x + 8y = −128 →
  21. 21.4x + 4y = 28 and 4x + 5y = 34 →
  22. 22.7x + y = −24 and x + 7y = 24 →
  23. 23.8x + 2y = 36 and 2x + 8y = 54 →
  24. 24.2x − y = 18 and 4x + 2y = 4 →
  25. 25.2x + 2y = 22 and 5x + y = 35 →
  26. 26.2x + 7y = −33 and 7x + 2y = −3 →
  27. 27.2x + 3y = 6 and 4x + 3y = −12 →
  28. 28.9x + 7y = −17 and 7x + 9y = −31 →
  29. 29.6x − y = 63 and 4x + y = 27 →
  30. 30.2x + 6y = 32 and 2x − y = 4 →
  31. 31.2x + 4y = −14 and 4x + 2y = −4 →
  32. 32.6x − 2y = −6 and x + 5y = 47 →
  33. 33.5x + 4y = 56 and x + 2y = 16 →
  34. 34.4x − 2y = −28 and 5x − 6y = −49 →
  35. 35.x + y = −1 and 5x + y = −9 →
  36. 36.3x + y = 24 and 5x − y = 32 →
  37. 37.9x + 6y = 6 and 6x + 9y = −6 →
  38. 38.6x + 8y = 34 and 8x + 6y = 50 →
  39. 39.x − 4y = −5 and 4x + 2y = −2 →
  40. 40.9x + 7y = −66 and 7x + 9y = −62 →

Answer key

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

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