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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 785 · 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. 1.7x + y = −47 and x + 7y = 7 →
  2. 2.x − 4y = 10 and 6x − 2y = 38 →
  3. 3.x − y = −5 and 2x − y = −1 →
  4. 4.5x + 7y = 48 and 7x + 5y = 48 →
  5. 5.7x + 5y = −6 and 5x + 7y = 6 →
  6. 6.8x + 6y = 32 and 6x + 8y = 38 →
  7. 7.2x + 2y = 2 and 4x + 6y = −10 →
  8. 8.3x + 5y = 39 and 2x + 4y = 28 →
  9. 9.8x + y = 25 and x + 8y = 11 →
  10. 10.5x + 2y = 39 and 2x + 5y = 24 →
  11. 11.x + 9y = −25 and 9x + y = 15 →
  12. 12.x + 2y = −6 and x − 6y = 2 →
  13. 13.4x + 2y = −12 and 3x + y = −7 →
  14. 14.5x + 2y = 33 and x − 3y = 10 →
  15. 15.x + y = 13 and 2x − 6y = −38 →
  16. 16.3x + 2y = −3 and 2x + 3y = −7 →
  17. 17.3x − 3y = 18 and 2x + 2y = −4 →
  18. 18.2x − 3y = −8 and 6x + 2y = −2 →
  19. 19.3x + 3y = 0 and 6x + 5y = 7 →
  20. 20.x + y = 3 and 3x − 5y = 1 →
  21. 21.x + 2y = 10 and 3x + y = 15 →
  22. 22.2x + 8y = 74 and 8x + 2y = 26 →
  23. 23.3x + 6y = 54 and 6x + 3y = 54 →
  24. 24.x + y = 13 and 2x + 4y = 42 →
  25. 25.5x − y = 25 and x − 4y = −14 →
  26. 26.x + 5y = 9 and 3x − 4y = −11 →
  27. 27.2x + 2y = 24 and 6x + 4y = 64 →
  28. 28.4x + 2y = 24 and 2x + 5y = 4 →
  29. 29.x + 6y = 2 and 6x + y = −23 →
  30. 30.9x + 3y = −18 and 3x + 9y = 66 →
  31. 31.4x + 2y = 46 and 3x + 2y = 37 →
  32. 32.4x + 3y = −39 and 2x + 4y = −32 →
  33. 33.6x + 7y = −34 and 7x + 6y = −44 →
  34. 34.8x + 5y = 29 and 5x + 8y = −16 →
  35. 35.3x + 7y = 37 and 7x + 3y = −7 →
  36. 36.7x + 3y = −40 and 3x + 7y = 0 →
  37. 37.2x + 2y = −10 and x + 6y = −35 →
  38. 38.6x + 6y = −6 and 6x − 6y = 66 →
  39. 39.3x − 3y = 0 and 2x + 2y = 12 →
  40. 40.3x − 5y = −43 and 2x − 6y = −50 →

Answer key

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

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