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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 297 · 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. 1.9x + y = 70 and x + 9y = 70 →
  2. 2.6x + 5y = 11 and 2x − 6y = −4 →
  3. 3.4x + 7y = −15 and 7x + 4y = −18 →
  4. 4.6x − 4y = −80 and x + 5y = 32 →
  5. 5.6x + 2y = −2 and 6x − 3y = −12 →
  6. 6.5x + 5y = 80 and 5x + 2y = 53 →
  7. 7.4x + y = −1 and 5x + 2y = 1 →
  8. 8.2x − 2y = −10 and 4x + 4y = 44 →
  9. 9.8x + 5y = 25 and 5x + 8y = 1 →
  10. 10.x + 5y = 30 and 5x + 2y = −11 →
  11. 11.x + 3y = −23 and 3x + y = −29 →
  12. 12.3x + 7y = −32 and 7x + 3y = 32 →
  13. 13.6x − 5y = −4 and 3x + y = −16 →
  14. 14.3x − 6y = −3 and 2x − y = 4 →
  15. 15.6x + 9y = 51 and 9x + 6y = 69 →
  16. 16.7x + y = −36 and x + 7y = 36 →
  17. 17.2x − 3y = −13 and 2x + 3y = 17 →
  18. 18.2x + 9y = 37 and 9x + 2y = 51 →
  19. 19.6x + 5y = 76 and 3x − 2y = 2 →
  20. 20.6x − 4y = 28 and 2x + 6y = −20 →
  21. 21.4x + 8y = −56 and 8x + 4y = −64 →
  22. 22.4x + 9y = −22 and 9x + 4y = 48 →
  23. 23.2x − 5y = 20 and 2x + 3y = 4 →
  24. 24.6x + 8y = −18 and 8x + 6y = 4 →
  25. 25.9x + 5y = 96 and 5x + 9y = 72 →
  26. 26.x − 2y = −1 and 3x + y = 18 →
  27. 27.4x + 2y = 2 and x + 4y = −3 →
  28. 28.6x − 5y = −38 and 4x + 6y = −44 →
  29. 29.6x − y = 9 and 5x + 3y = 19 →
  30. 30.5x + 5y = 20 and x + 6y = −16 →
  31. 31.2x + 6y = 28 and 6x + 2y = 52 →
  32. 32.3x + 6y = 48 and 6x + 3y = 33 →
  33. 33.9x + 3y = 45 and 3x + 9y = 39 →
  34. 34.6x − 5y = 23 and 2x − 3y = 1 →
  35. 35.x − 5y = −37 and 2x − 2y = −10 →
  36. 36.3x + 4y = 43 and 5x + 2y = 53 →
  37. 37.7x + 6y = 10 and 6x + 7y = 16 →
  38. 38.6x + 2y = 16 and x − 5y = 40 →
  39. 39.x + 2y = −7 and 3x + 4y = −11 →
  40. 40.6x + 2y = 44 and 5x + 2y = 38 →

Answer key

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

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