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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 122 · 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 = −32 and 4x + 4y = −16 →
  2. 2.x + 3y = −14 and 3x + y = −10 →
  3. 3.5x + 3y = 33 and 3x + 5y = 23 →
  4. 4.2x + 6y = −64 and x + 6y = −56 →
  5. 5.5x − 2y = −47 and 3x + 5y = 9 →
  6. 6.3x + 4y = 0 and 4x + 3y = −14 →
  7. 7.6x + 9y = 54 and 9x + 6y = 51 →
  8. 8.9x + 3y = 75 and 3x + 9y = 57 →
  9. 9.2x + 6y = −26 and 5x + 5y = −5 →
  10. 10.8x + 4y = 60 and 4x + 8y = 84 →
  11. 11.5x − 3y = 0 and 3x − 4y = −11 →
  12. 12.9x + 2y = 68 and 2x + 9y = −2 →
  13. 13.2x + 4y = 16 and 3x − 2y = 8 →
  14. 14.5x + y = −17 and x + 5y = −13 →
  15. 15.2x + 6y = 44 and 3x − 3y = −18 →
  16. 16.x + 8y = 48 and 8x + y = −57 →
  17. 17.3x + 5y = 57 and 2x + 6y = 54 →
  18. 18.x + 5y = 11 and 5x + y = 31 →
  19. 19.3x + 2y = 34 and 2x + 6y = 60 →
  20. 20.x + 2y = 12 and 6x − 6y = −54 →
  21. 21.6x + 4y = −62 and 4x + 6y = −48 →
  22. 22.3x + y = −10 and 2x + 2y = −4 →
  23. 23.2x − 4y = −16 and 5x + 2y = −28 →
  24. 24.4x + 6y = 42 and 6x + 4y = 38 →
  25. 25.x + 3y = −5 and 6x − 4y = 36 →
  26. 26.x + 5y = −26 and 4x + 3y = −36 →
  27. 27.5x − y = 7 and 4x − y = 5 →
  28. 28.5x + 6y = −21 and x + 4y = −7 →
  29. 29.2x − 6y = 20 and 2x − y = 10 →
  30. 30.2x − 4y = −14 and 4x − 5y = −13 →
  31. 31.4x − y = −8 and x + 2y = −11 →
  32. 32.5x + 3y = 35 and 6x − 6y = −6 →
  33. 33.3x + y = 18 and x + 3y = 22 →
  34. 34.3x + y = −13 and x + 3y = −23 →
  35. 35.4x + 3y = 60 and x + y = 17 →
  36. 36.2x − 5y = −28 and 6x + 4y = 30 →
  37. 37.4x − 4y = −36 and 5x + 4y = 0 →
  38. 38.x + 3y = 27 and 3x + y = 25 →
  39. 39.6x + 6y = 30 and 3x − 3y = 21 →
  40. 40.9x + 3y = −48 and 3x + 9y = 0 →

Answer key

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

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