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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 790 · 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 − 2y = 10 and 5x − 5y = −5 →
  2. 2.x + 5y = −13 and 4x + y = 24 →
  3. 3.x + 6y = −27 and 6x − 5y = 43 →
  4. 4.4x − 5y = 51 and x − 5y = 39 →
  5. 5.3x + 3y = −24 and 3x + 5y = −28 →
  6. 6.5x + y = 6 and 5x − 4y = 1 →
  7. 7.6x − y = −45 and 4x + 4y = 12 →
  8. 8.3x − 5y = −33 and 3x + y = −15 →
  9. 9.3x − 2y = −22 and 2x + 6y = −22 →
  10. 10.8x + y = −12 and x + 8y = 30 →
  11. 11.x + 3y = 26 and 3x − 2y = −10 →
  12. 12.9x + 4y = 7 and 4x + 9y = 32 →
  13. 13.5x − 3y = 0 and x + 4y = 23 →
  14. 14.2x + y = −9 and 5x − 2y = −27 →
  15. 15.x + 9y = −65 and 9x + y = 55 →
  16. 16.x + 7y = −22 and 7x + y = −10 →
  17. 17.3x − 5y = −7 and 3x − 6y = −9 →
  18. 18.4x − y = −12 and 5x + 2y = 11 →
  19. 19.2x + 9y = 74 and 9x + 2y = 25 →
  20. 20.4x + 2y = −26 and 2x + 4y = −4 →
  21. 21.9x + 5y = −13 and 5x + 9y = −57 →
  22. 22.5x − 2y = 1 and 2x − 3y = −4 →
  23. 23.4x − 2y = 18 and 6x + 2y = 42 →
  24. 24.3x + 3y = 18 and 4x − y = 14 →
  25. 25.4x + y = 21 and 4x + 3y = 39 →
  26. 26.4x − 2y = 4 and 4x + y = 16 →
  27. 27.3x + 9y = −66 and 9x + 3y = −78 →
  28. 28.5x + 2y = 29 and x + 6y = 45 →
  29. 29.5x + y = −14 and 4x + 2y = −22 →
  30. 30.2x + 9y = 48 and 9x + 2y = 62 →
  31. 31.4x + 3y = −31 and 2x + 4y = −38 →
  32. 32.2x − y = 1 and x − 6y = 50 →
  33. 33.5x + 8y = −92 and 8x + 5y = −77 →
  34. 34.6x + 3y = 27 and 5x + 5y = 25 →
  35. 35.4x + y = −28 and 3x − y = −7 →
  36. 36.5x + 5y = 20 and 4x + 5y = 18 →
  37. 37.4x + y = 10 and 3x + y = 7 →
  38. 38.5x + 3y = −21 and 6x + 5y = −28 →
  39. 39.2x + 3y = 25 and 3x − 3y = −30 →
  40. 40.x − 2y = 12 and x − 3y = 19 →

Answer key

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

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