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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 118 · 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 + 9y = 2 and 9x + 5y = 26 →
  2. 2.6x + 8y = −14 and 8x + 6y = −28 →
  3. 3.6x + y = 15 and 6x + 4y = 24 →
  4. 4.4x + 2y = 10 and 2x + 4y = 8 →
  5. 5.5x + 2y = 28 and 2x + 6y = 58 →
  6. 6.3x − 6y = 12 and x − 6y = 8 →
  7. 7.5x − 2y = −8 and 4x − 3y = −19 →
  8. 8.8x + 2y = 56 and 2x + 8y = 74 →
  9. 9.2x − 3y = −32 and 4x + y = −8 →
  10. 10.4x + 8y = 40 and 8x + 4y = 32 →
  11. 11.5x + y = −2 and x + 5y = 14 →
  12. 12.x − 2y = 13 and 6x + 2y = 50 →
  13. 13.9x + 6y = 30 and 6x + 9y = 0 →
  14. 14.9x + 8y = −76 and 8x + 9y = −77 →
  15. 15.2x + 3y = −5 and 3x + 2y = −5 →
  16. 16.3x + 6y = 18 and 6x + y = 14 →
  17. 17.4x + 4y = 0 and 3x − 3y = 54 →
  18. 18.6x + y = 39 and x + y = 4 →
  19. 19.7x + 5y = −38 and 5x + 7y = −58 →
  20. 20.4x + 5y = 43 and 4x − 4y = −20 →
  21. 21.4x − 6y = 38 and 5x + 3y = 37 →
  22. 22.x + 5y = 6 and 4x − 2y = 2 →
  23. 23.3x + 2y = 14 and 5x + 6y = 34 →
  24. 24.x − y = −6 and 2x + y = 0 →
  25. 25.4x + 3y = −27 and 3x + 4y = −15 →
  26. 26.2x + 8y = 68 and 8x + 2y = 32 →
  27. 27.x + 3y = 12 and 3x + 4y = 21 →
  28. 28.x − 2y = 6 and 3x − 2y = −2 →
  29. 29.3x + 2y = 27 and 2x + 6y = 60 →
  30. 30.5x − 2y = 27 and 4x + 6y = 52 →
  31. 31.9x + 5y = 40 and 5x + 9y = 16 →
  32. 32.2x + 3y = −14 and 3x + 2y = −6 →
  33. 33.4x + 2y = −6 and 6x − 6y = −18 →
  34. 34.2x + 4y = 50 and 6x + 2y = 70 →
  35. 35.x + 6y = 15 and 2x + 6y = 24 →
  36. 36.4x + 3y = 33 and 3x + 4y = 30 →
  37. 37.2x + 5y = 3 and 5x + 2y = −3 →
  38. 38.8x + 2y = −28 and 2x + 8y = 38 →
  39. 39.2x + 8y = 30 and 8x + 2y = −30 →
  40. 40.3x − 6y = −42 and 2x + y = −3 →

Answer key

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

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