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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 235 · 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 + 5y = 35 and 2x − 3y = −6 →
  2. 2.x + 3y = 22 and 4x + 5y = 46 →
  3. 3.9x + 8y = 55 and 8x + 9y = 47 →
  4. 4.3x + y = 22 and 2x − y = 8 →
  5. 5.2x + 6y = 46 and 6x + 6y = 78 →
  6. 6.6x − y = 16 and 5x + 4y = 52 →
  7. 7.x + 6y = 55 and 6x + y = 15 →
  8. 8.5x + 2y = 37 and 2x + 5y = 40 →
  9. 9.9x + 7y = −83 and 7x + 9y = −93 →
  10. 10.3x + 5y = −8 and 2x + 5y = −12 →
  11. 11.4x − 5y = −11 and 4x − 4y = −16 →
  12. 12.9x + y = 10 and x + 9y = 10 →
  13. 13.2x − 3y = −4 and 6x + y = 8 →
  14. 14.x + 4y = 12 and 5x − 5y = 35 →
  15. 15.x + 2y = 21 and 2x + 5y = 48 →
  16. 16.x + 5y = 16 and 5x + y = 32 →
  17. 17.2x + 4y = −4 and 3x + 2y = −10 →
  18. 18.8x + 2y = 44 and 2x + 8y = −4 →
  19. 19.5x + 7y = −26 and 7x + 5y = 2 →
  20. 20.x − 4y = −14 and 4x + 4y = 4 →
  21. 21.5x + y = 39 and x + 5y = 51 →
  22. 22.7x + 4y = 84 and 4x + 7y = 81 →
  23. 23.6x − 5y = −1 and x + y = 9 →
  24. 24.x − 3y = 35 and x + 3y = −19 →
  25. 25.x + 9y = 70 and 9x + y = −10 →
  26. 26.x + 4y = −24 and 4x + y = −21 →
  27. 27.2x − 6y = −42 and 3x − y = −15 →
  28. 28.4x − y = −27 and 2x + y = −9 →
  29. 29.5x + 3y = 43 and x − 4y = −19 →
  30. 30.4x + y = −30 and 3x − 3y = −30 →
  31. 31.x + 2y = 4 and 3x + 5y = 7 →
  32. 32.9x + 6y = −117 and 6x + 9y = −123 →
  33. 33.5x − 5y = −60 and 6x − 4y = −60 →
  34. 34.2x + y = −1 and 4x + 3y = 7 →
  35. 35.x + 7y = 51 and 7x + y = 21 →
  36. 36.4x − 2y = −10 and 4x + y = −19 →
  37. 37.5x + 2y = 19 and 4x + 5y = −12 →
  38. 38.5x + 3y = 21 and 5x − 6y = 93 →
  39. 39.7x + 4y = 17 and 4x + 7y = −28 →
  40. 40.3x − 5y = −28 and 2x + 6y = 28 →

Answer key

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

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