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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 668 · 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. 1.6x + y = 57 and 2x + 4y = 30 →
  2. 2.3x + 6y = −42 and 6x + 3y = −3 →
  3. 3.2x + 2y = 6 and 4x + y = 18 →
  4. 4.3x − 2y = 28 and x + 4y = −14 →
  5. 5.6x − y = −13 and 4x + 5y = −3 →
  6. 6.3x + 8y = −44 and 8x + 3y = 11 →
  7. 7.3x − 4y = −15 and 4x + 6y = 48 →
  8. 8.2x − 5y = 37 and 4x + 6y = −38 →
  9. 9.6x + 3y = 18 and 4x + 3y = 14 →
  10. 10.4x + 5y = 37 and x + y = 8 →
  11. 11.2x − y = −27 and x − 4y = −45 →
  12. 12.6x + y = 53 and 5x − y = 35 →
  13. 13.9x + y = 61 and x + 9y = 69 →
  14. 14.6x + 3y = 51 and 5x + y = 35 →
  15. 15.3x + y = −12 and x + 3y = 4 →
  16. 16.x + 3y = −21 and 2x + y = −2 →
  17. 17.x + y = 0 and 2x + 6y = −16 →
  18. 18.x + 4y = 11 and 4x + y = 14 →
  19. 19.x + 8y = 24 and 8x + y = 66 →
  20. 20.6x + 3y = −27 and 2x + 4y = 0 →
  21. 21.5x + 3y = 55 and 3x − 3y = 9 →
  22. 22.3x + y = 11 and 5x + 4y = 9 →
  23. 23.9x + 5y = 47 and 5x + 9y = 51 →
  24. 24.9x + 8y = 40 and 8x + 9y = 28 →
  25. 25.8x + 4y = −8 and 4x + 8y = 20 →
  26. 26.3x + 4y = 14 and 4x + 3y = 14 →
  27. 27.2x + 8y = 64 and 8x + 2y = 46 →
  28. 28.6x + 4y = −32 and 4x + 6y = −38 →
  29. 29.x − 3y = 21 and x − 6y = 33 →
  30. 30.6x + 7y = −2 and 7x + 6y = −11 →
  31. 31.x + y = 11 and 4x + 2y = 26 →
  32. 32.4x + 3y = 25 and 4x − y = −3 →
  33. 33.3x + y = 24 and 3x + 3y = 30 →
  34. 34.5x + 2y = −19 and x + 4y = 25 →
  35. 35.3x + 6y = 51 and 4x + 4y = 40 →
  36. 36.6x + 5y = −14 and x + 3y = −11 →
  37. 37.5x + 7y = −13 and 7x + 5y = 1 →
  38. 38.5x − y = −12 and 4x − 3y = −14 →
  39. 39.9x + 8y = 129 and 8x + 9y = 126 →
  40. 40.x − 6y = −9 and 5x + y = −14 →

Answer key

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

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