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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 176 · 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 + 3y = 27 and 2x + 5y = 21 →
  2. 2.3x − 5y = 26 and 4x + 6y = 22 →
  3. 3.9x + 6y = 57 and 6x + 9y = 78 →
  4. 4.2x + 5y = 6 and x − 3y = −19 →
  5. 5.2x + 2y = 0 and 2x − 2y = −20 →
  6. 6.4x + 3y = 5 and 3x + 4y = 9 →
  7. 7.7x + y = −34 and x + 7y = 2 →
  8. 8.6x + 4y = 50 and 4x + 4y = 44 →
  9. 9.4x + 5y = 18 and x + 5y = 27 →
  10. 10.7x + 2y = −52 and 2x + 7y = −2 →
  11. 11.2x − y = 1 and 6x − 4y = 2 →
  12. 12.4x + 9y = −4 and 9x + 4y = 56 →
  13. 13.3x + y = −18 and 2x − 4y = −54 →
  14. 14.x + 2y = 19 and 3x − 6y = −27 →
  15. 15.6x + y = 37 and 4x + y = 25 →
  16. 16.5x + y = 7 and 6x − 3y = 21 →
  17. 17.4x + 5y = 7 and x + 6y = 35 →
  18. 18.6x + 2y = 20 and x − y = −2 →
  19. 19.5x + 2y = 20 and 2x + 5y = 29 →
  20. 20.5x − y = 27 and 6x − 5y = 40 →
  21. 21.5x + 7y = 27 and 7x + 5y = 9 →
  22. 22.x + y = −6 and 2x − 6y = 60 →
  23. 23.3x − 2y = −13 and 4x + 5y = −71 →
  24. 24.5x + 3y = 1 and 3x + 5y = −9 →
  25. 25.5x + 3y = 14 and 3x + 5y = −14 →
  26. 26.6x − 3y = −66 and 3x − 4y = −53 →
  27. 27.3x − 5y = −44 and 6x + y = −11 →
  28. 28.9x + 8y = 35 and 8x + 9y = 33 →
  29. 29.5x + 3y = 16 and 5x − y = 8 →
  30. 30.4x + 5y = 38 and 4x + 2y = 32 →
  31. 31.5x − 3y = 6 and 2x − 6y = 36 →
  32. 32.2x − y = −27 and 5x − 4y = −81 →
  33. 33.x + 5y = 26 and 5x + y = −14 →
  34. 34.2x − 6y = −14 and x + 2y = 13 →
  35. 35.6x − 4y = 18 and 5x − 5y = 0 →
  36. 36.5x + 6y = −14 and 2x − 5y = 24 →
  37. 37.2x + 6y = 4 and 6x + y = −22 →
  38. 38.8x + 5y = 3 and 5x + 8y = −3 →
  39. 39.9x + 7y = −38 and 7x + 9y = −58 →
  40. 40.9x + 3y = 42 and 3x + 9y = −42 →

Answer key

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

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