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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 391 · 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 = −14 and 2x + 4y = 42 →
  2. 2.3x + 2y = 8 and 3x + 6y = −12 →
  3. 3.2x + 2y = 4 and 6x + y = −8 →
  4. 4.x + 3y = −28 and 3x + y = −20 →
  5. 5.6x + 2y = 24 and x − y = 8 →
  6. 6.7x + 4y = 1 and 4x + 7y = 10 →
  7. 7.2x + 7y = −3 and 7x + 2y = −33 →
  8. 8.x + 8y = 11 and 8x + y = −38 →
  9. 9.8x + 9y = 64 and 9x + 8y = 55 →
  10. 10.4x + y = 35 and 3x + 2y = 30 →
  11. 11.9x + 5y = 43 and 5x + 9y = 55 →
  12. 12.2x + 4y = −32 and 4x + 5y = −37 →
  13. 13.x − y = −4 and 2x + 2y = 16 →
  14. 14.5x − 5y = 35 and 3x + 5y = 37 →
  15. 15.2x + 2y = 12 and 4x + 2y = 28 →
  16. 16.4x + 3y = −32 and 6x − 5y = −10 →
  17. 17.2x − y = −19 and 3x + y = −26 →
  18. 18.6x + 2y = 18 and 2x + 6y = 38 →
  19. 19.2x + 4y = −16 and 2x − 3y = −2 →
  20. 20.2x + y = 12 and x + 2y = 15 →
  21. 21.4x + 5y = 23 and 3x + 4y = 18 →
  22. 22.9x + 7y = 95 and 7x + 9y = 81 →
  23. 23.x + 3y = 8 and 3x + 5y = 12 →
  24. 24.x − 4y = −19 and 2x − y = −3 →
  25. 25.5x + 6y = −47 and 6x + 5y = −52 →
  26. 26.2x + 6y = 14 and 6x − 2y = −18 →
  27. 27.5x + 4y = 33 and 4x + y = 22 →
  28. 28.6x + y = 22 and 5x − y = 11 →
  29. 29.x + y = 17 and 4x + y = 41 →
  30. 30.2x + 2y = 14 and x − y = 5 →
  31. 31.2x + 4y = −2 and 4x + 2y = 8 →
  32. 32.2x + y = −10 and x + 2y = −11 →
  33. 33.3x − 6y = −6 and x + 3y = 13 →
  34. 34.6x + 2y = 34 and 4x + 3y = 31 →
  35. 35.x − 5y = −45 and 2x − y = −18 →
  36. 36.4x − 3y = −2 and 4x + 4y = 12 →
  37. 37.9x + 5y = −34 and 5x + 9y = −50 →
  38. 38.3x + 9y = 6 and 9x + 3y = 42 →
  39. 39.7x + y = −32 and x + 7y = 16 →
  40. 40.5x − y = −27 and 5x − 5y = −15 →

Answer key

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

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