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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 722 · 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 + 6y = −1 and 6x − 6y = 36 →
  2. 2.4x + 3y = 39 and x − 3y = 6 →
  3. 3.5x + 2y = 21 and 5x − 2y = −11 →
  4. 4.3x − 6y = 27 and 2x − y = 15 →
  5. 5.8x + 2y = 46 and 2x + 8y = −56 →
  6. 6.x − y = 11 and 5x + 3y = −1 →
  7. 7.2x + y = −11 and x + 2y = 2 →
  8. 8.8x + y = 73 and x + 8y = 80 →
  9. 9.6x + 2y = 44 and 4x + 5y = 33 →
  10. 10.7x + 2y = 32 and 2x + 7y = −23 →
  11. 11.3x + 6y = 42 and 6x + 3y = 57 →
  12. 12.5x − 2y = −6 and x + 5y = 42 →
  13. 13.2x − y = 2 and 6x − 2y = 0 →
  14. 14.x + 5y = −42 and 5x + y = 6 →
  15. 15.6x − 5y = −13 and x + 6y = −50 →
  16. 16.3x + 4y = 27 and 4x − 2y = −8 →
  17. 17.x + 6y = 45 and 5x − 2y = 1 →
  18. 18.5x + 6y = 43 and 5x − 5y = −45 →
  19. 19.4x − 4y = 4 and 4x − y = 19 →
  20. 20.3x − 5y = −1 and 6x − y = −38 →
  21. 21.2x + 6y = −14 and 6x + 2y = 38 →
  22. 22.2x + 7y = −7 and 7x + 2y = 43 →
  23. 23.4x − 4y = 28 and 4x + 2y = 40 →
  24. 24.4x + 4y = 56 and 6x + 3y = 63 →
  25. 25.5x + 2y = 48 and 2x + 5y = 36 →
  26. 26.x + 2y = 12 and 5x + 2y = 28 →
  27. 27.2x + y = 11 and 2x + 6y = 46 →
  28. 28.9x + 3y = 78 and 3x + 9y = 66 →
  29. 29.3x + 3y = 18 and 2x + 5y = 21 →
  30. 30.8x + 2y = 40 and 2x + 8y = 40 →
  31. 31.7x + y = −43 and x + 7y = 35 →
  32. 32.5x − 3y = −26 and 6x + 5y = −14 →
  33. 33.2x + 4y = 54 and 4x + 3y = 63 →
  34. 34.6x + 5y = 38 and x + 2y = 11 →
  35. 35.4x − 5y = 73 and 5x + 4y = −1 →
  36. 36.2x + 9y = 25 and 9x + 2y = −3 →
  37. 37.2x + 3y = 28 and 4x + 5y = 50 →
  38. 38.9x + 8y = 52 and 8x + 9y = 50 →
  39. 39.8x + 2y = 52 and 2x + 8y = −32 →
  40. 40.x + 6y = 37 and x − y = −5 →

Answer key

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

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