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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 477 · 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 + 5y = 7 and 4x + y = −29 →
  2. 2.3x + 2y = 7 and 2x − 2y = 18 →
  3. 3.x − 3y = 9 and 5x − 5y = −5 →
  4. 4.2x + 7y = 61 and 7x + 2y = 11 →
  5. 5.x + 6y = 13 and 5x − 5y = −5 →
  6. 6.2x − 4y = −14 and x + y = 14 →
  7. 7.5x − y = −37 and x − 6y = 39 →
  8. 8.2x + 6y = −40 and 5x + 5y = −30 →
  9. 9.4x − 3y = 16 and 3x − 4y = 26 →
  10. 10.7x + y = 12 and x + 7y = −60 →
  11. 11.x + 6y = −22 and 3x + y = 2 →
  12. 12.4x + 4y = 24 and 2x + 4y = 8 →
  13. 13.6x − 6y = −6 and 2x − y = −3 →
  14. 14.2x + 3y = 8 and 3x + 6y = 9 →
  15. 15.x + 5y = −33 and 2x − 5y = 39 →
  16. 16.4x + 5y = 28 and x + 4y = 18 →
  17. 17.4x + 8y = −76 and 8x + 4y = −44 →
  18. 18.2x − 4y = −20 and 3x + 3y = 24 →
  19. 19.4x + y = 11 and 6x + 4y = 34 →
  20. 20.4x + 5y = 24 and 2x − 3y = −10 →
  21. 21.3x − 4y = 32 and 6x + 2y = 44 →
  22. 22.2x + 5y = −38 and 5x + 2y = −32 →
  23. 23.6x + 3y = 33 and x + 3y = −7 →
  24. 24.4x − 5y = 52 and 5x − 6y = 64 →
  25. 25.5x − 2y = −4 and 4x − 6y = 10 →
  26. 26.x + 3y = 15 and 3x + y = −3 →
  27. 27.x + 5y = 26 and x + 2y = 8 →
  28. 28.9x + 5y = −42 and 5x + 9y = 14 →
  29. 29.5x + 5y = −20 and 4x − y = 14 →
  30. 30.6x − y = 5 and 5x − 6y = −1 →
  31. 31.6x + 6y = −54 and 6x + 5y = −51 →
  32. 32.5x + 2y = 24 and 2x + 5y = 39 →
  33. 33.4x + 2y = 6 and 2x + 4y = 6 →
  34. 34.2x + y = 1 and x − y = 5 →
  35. 35.2x + 5y = 16 and 5x + 3y = −17 →
  36. 36.6x − 3y = −69 and 2x − 6y = −58 →
  37. 37.5x − y = 38 and 3x + y = 10 →
  38. 38.4x + 6y = 26 and 6x + 4y = 34 →
  39. 39.5x − 4y = −22 and 2x − 3y = −6 →
  40. 40.4x + 6y = 10 and 6x + 2y = 22 →

Answer key

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

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