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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 650 · 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.x − 3y = 23 and 5x − 3y = 55 →
  2. 2.2x − 2y = 6 and 4x + 2y = 48 →
  3. 3.2x − 6y = 66 and 5x + 2y = 29 →
  4. 4.2x + 6y = 6 and 5x − 2y = −36 →
  5. 5.6x + 3y = 27 and 3x − 3y = 36 →
  6. 6.7x + 4y = 59 and 4x + 7y = 29 →
  7. 7.2x + 6y = 14 and x + 6y = 16 →
  8. 8.5x + y = 16 and 5x + 5y = −20 →
  9. 9.x − 2y = 17 and 2x + 3y = −15 →
  10. 10.3x + 5y = 44 and 2x − 5y = −29 →
  11. 11.2x + 4y = 34 and x + 6y = 33 →
  12. 12.2x + 4y = −32 and 4x + 4y = −44 →
  13. 13.4x + y = 3 and x + 4y = −3 →
  14. 14.x − y = 9 and 2x − 4y = 30 →
  15. 15.x + y = 2 and 2x + 5y = 7 →
  16. 16.4x + 2y = 52 and 6x + 6y = 102 →
  17. 17.2x − 3y = −1 and 4x + 2y = 38 →
  18. 18.x + 6y = 3 and 6x + y = −52 →
  19. 19.x + 4y = −27 and 4x − 4y = 72 →
  20. 20.7x + 5y = 72 and 5x + 7y = 72 →
  21. 21.2x + 6y = 4 and 5x + 2y = 36 →
  22. 22.6x + 3y = 27 and 5x + 3y = 18 →
  23. 23.9x + 5y = 38 and 5x + 9y = 46 →
  24. 24.8x + 5y = 18 and 5x + 8y = 21 →
  25. 25.7x + 6y = 90 and 6x + 7y = 92 →
  26. 26.5x − 2y = −7 and 3x − 2y = −9 →
  27. 27.2x + 6y = 50 and 5x − 6y = −1 →
  28. 28.7x + 5y = 33 and 5x + 7y = 3 →
  29. 29.x + 5y = −6 and 5x + y = 42 →
  30. 30.4x − 2y = 20 and 3x − 4y = 5 →
  31. 31.7x + 3y = 16 and 3x + 7y = −16 →
  32. 32.6x + 3y = −24 and 5x + y = −23 →
  33. 33.6x + 5y = 18 and 5x + 6y = 4 →
  34. 34.3x + y = 5 and 6x + y = 8 →
  35. 35.x + 2y = 13 and 6x − 2y = 8 →
  36. 36.x − 2y = −2 and 2x − 5y = −7 →
  37. 37.5x + 5y = 0 and 5x + 3y = −6 →
  38. 38.7x + 3y = −4 and 3x + 7y = 4 →
  39. 39.x + y = 6 and 2x − 3y = −23 →
  40. 40.4x + 7y = 50 and 7x + 4y = 38 →

Answer key

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

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