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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 259 · 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. 1.4x − 4y = 40 and 2x − y = 15 →
  2. 2.3x + 4y = −25 and 5x + 2y = −9 →
  3. 3.x + 2y = 4 and 2x − y = 18 →
  4. 4.6x + 5y = 0 and 2x − y = −16 →
  5. 5.6x − 6y = −66 and 2x + y = 2 →
  6. 6.2x − 5y = −28 and 3x − 6y = −39 →
  7. 7.x + 2y = 17 and x + 3y = 25 →
  8. 8.x + 3y = −19 and 3x + y = −17 →
  9. 9.9x + 2y = −30 and 2x + 9y = 19 →
  10. 10.5x + 4y = 62 and 4x − y = 16 →
  11. 11.9x + y = 48 and x + 9y = 32 →
  12. 12.6x − y = −12 and 5x + 5y = 25 →
  13. 13.2x + 6y = −20 and 3x + 2y = −2 →
  14. 14.6x − 4y = −10 and 6x + 4y = −74 →
  15. 15.6x + 6y = −42 and 2x − 2y = −6 →
  16. 16.4x + 3y = −25 and 4x + 6y = −46 →
  17. 17.5x + 2y = 43 and 5x − 5y = 50 →
  18. 18.2x − y = 10 and x + 3y = −23 →
  19. 19.3x + 6y = 57 and 5x − 6y = −49 →
  20. 20.4x − 5y = −13 and 5x − 3y = 13 →
  21. 21.3x + 9y = −15 and 9x + 3y = 3 →
  22. 22.x − 3y = 22 and 5x + 3y = −16 →
  23. 23.2x + 3y = 30 and 3x + 5y = 49 →
  24. 24.3x + 5y = −54 and 5x + 2y = −52 →
  25. 25.4x + 6y = −32 and 3x − y = 20 →
  26. 26.4x + 6y = 66 and 5x − 5y = 20 →
  27. 27.5x + 6y = −55 and 3x + 4y = −35 →
  28. 28.x + 4y = −17 and 4x + y = 7 →
  29. 29.5x + y = 9 and 4x − 6y = 14 →
  30. 30.6x + y = 7 and x + 6y = 7 →
  31. 31.7x + 5y = 18 and 5x + 7y = 6 →
  32. 32.x + 6y = 35 and 4x + y = −21 →
  33. 33.9x + 2y = −20 and 2x + 9y = −13 →
  34. 34.x + 6y = 13 and 6x + y = 43 →
  35. 35.2x + 2y = −26 and 2x − 5y = 16 →
  36. 36.8x + 6y = 36 and 6x + 8y = 20 →
  37. 37.5x + 9y = 71 and 9x + 5y = 27 →
  38. 38.2x + 4y = 42 and 2x + 5y = 48 →
  39. 39.5x + y = 38 and 4x + 2y = 34 →
  40. 40.7x + 5y = 103 and 5x + 7y = 101 →

Answer key

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

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