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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 917 · 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. 1.5x + 4y = −32 and 4x + 5y = −22 →
  2. 2.3x + 8y = 14 and 8x + 3y = 19 →
  3. 3.4x + 5y = 40 and 5x + 3y = 37 →
  4. 4.2x + 5y = −2 and x + 6y = −15 →
  5. 5.5x + 4y = 41 and x + 4y = 21 →
  6. 6.4x + 8y = 52 and 8x + 4y = 56 →
  7. 7.2x + 5y = 20 and 4x − 4y = 12 →
  8. 8.2x + 6y = 62 and 2x + 2y = 30 →
  9. 9.2x + 8y = 42 and 8x + 2y = 18 →
  10. 10.3x + 3y = −21 and 6x + 5y = −37 →
  11. 11.3x − y = −12 and 2x + 3y = −41 →
  12. 12.2x + 4y = −28 and x − 4y = 34 →
  13. 13.x + 5y = 9 and 2x + 2y = 2 →
  14. 14.6x + 2y = −16 and 3x − 4y = 17 →
  15. 15.2x + 3y = −16 and 3x + 2y = −4 →
  16. 16.2x − y = −1 and 6x − 4y = 6 →
  17. 17.x + 3y = 18 and 6x − 4y = 42 →
  18. 18.9x + 2y = 60 and 2x + 9y = −38 →
  19. 19.3x + 5y = 3 and 2x + 2y = 6 →
  20. 20.3x + 2y = −19 and 2x + 3y = −11 →
  21. 21.2x + 2y = −8 and 2x + 6y = 4 →
  22. 22.2x + 6y = 0 and 6x + 2y = −48 →
  23. 23.4x + 2y = 20 and 2x + 4y = −8 →
  24. 24.4x + 6y = 40 and 4x − 6y = −32 →
  25. 25.4x − 4y = 8 and 3x + y = −6 →
  26. 26.6x + 7y = 62 and 7x + 6y = 68 →
  27. 27.5x + 2y = 44 and 6x − 5y = 38 →
  28. 28.4x + 4y = −36 and 2x − 3y = 12 →
  29. 29.x − 5y = 23 and 6x + 2y = 10 →
  30. 30.2x − 3y = −19 and x + 6y = 28 →
  31. 31.2x + 4y = −38 and 3x + 3y = −33 →
  32. 32.3x − y = 19 and 2x − 5y = −22 →
  33. 33.9x + 2y = 26 and 2x + 9y = −37 →
  34. 34.2x + 6y = 68 and x − y = −2 →
  35. 35.4x − 6y = 64 and 5x − 3y = 44 →
  36. 36.3x + 3y = −15 and 6x − 5y = 14 →
  37. 37.6x − y = −34 and 2x + 3y = −18 →
  38. 38.9x + 7y = 32 and 7x + 9y = 32 →
  39. 39.8x + 2y = −2 and 2x + 8y = −68 →
  40. 40.x + 2y = −1 and 2x + y = −8 →

Answer key

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

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