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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 482 · 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 + 7y = 5 and 7x + 6y = 21 →
  2. 2.5x + 2y = −4 and 6x + 4y = 0 →
  3. 3.6x + 5y = −67 and 2x + y = −19 →
  4. 4.x − 3y = 32 and 2x − y = 24 →
  5. 5.9x + 2y = −4 and 2x + 9y = 59 →
  6. 6.9x + 4y = 104 and 4x + 9y = 104 →
  7. 7.6x + 6y = −6 and 4x + 5y = −12 →
  8. 8.6x − y = 9 and 2x + 3y = 33 →
  9. 9.6x + 4y = 62 and 5x + 6y = 57 →
  10. 10.5x + 2y = 11 and 2x + 5y = −4 →
  11. 11.x + 2y = 10 and 5x − 6y = 18 →
  12. 12.4x + y = −26 and 6x + 6y = −48 →
  13. 13.x + 3y = −26 and 3x + y = −6 →
  14. 14.2x − 3y = 10 and 6x + 6y = 60 →
  15. 15.x + 3y = 27 and x − 2y = −3 →
  16. 16.2x + 5y = −12 and 5x + 4y = 4 →
  17. 17.6x + 2y = 66 and 3x − y = 15 →
  18. 18.6x + 4y = 38 and 5x − 2y = 21 →
  19. 19.3x + 3y = 6 and x − 6y = −54 →
  20. 20.4x − 5y = −17 and 5x − y = 26 →
  21. 21.x − 5y = 42 and 4x + 3y = 7 →
  22. 22.2x + 8y = 2 and 8x + 2y = −52 →
  23. 23.2x + 3y = 9 and 2x + y = 7 →
  24. 24.x + 5y = 26 and 2x − 3y = 0 →
  25. 25.4x + 6y = −26 and 6x + y = 17 →
  26. 26.4x + 5y = 27 and x + 4y = 15 →
  27. 27.2x + 7y = 19 and 7x + 2y = 44 →
  28. 28.3x + y = −9 and x + 3y = 5 →
  29. 29.3x − 4y = −1 and 2x + 5y = −39 →
  30. 30.x − 2y = −8 and 3x − y = 16 →
  31. 31.6x + 2y = 28 and 4x − 6y = 26 →
  32. 32.2x + 5y = 57 and 5x + 2y = 48 →
  33. 33.6x + 4y = 36 and 6x + 2y = 24 →
  34. 34.3x + y = 22 and 5x − 2y = 33 →
  35. 35.4x − 4y = −8 and 6x + y = −5 →
  36. 36.2x − 5y = −6 and x − 2y = −4 →
  37. 37.5x + 5y = −30 and 3x + y = −10 →
  38. 38.6x − 4y = −74 and 2x + 2y = −8 →
  39. 39.x + 2y = 3 and 2x − 5y = −12 →
  40. 40.9x + 7y = −13 and 7x + 9y = −3 →

Answer key

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

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