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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 856 · 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 + 7y = 50 and 7x + y = 62 →
  2. 2.6x + 4y = 4 and x + 2y = −6 →
  3. 3.6x + 4y = 26 and 5x + 6y = 27 →
  4. 4.x + 4y = 21 and 6x + 4y = 46 →
  5. 5.8x + 5y = 24 and 5x + 8y = 54 →
  6. 6.3x + 5y = 6 and 5x + 3y = −22 →
  7. 7.5x + 3y = 13 and 3x + 5y = 11 →
  8. 8.x + 2y = 4 and x − 4y = −2 →
  9. 9.x + 4y = −7 and 5x − 6y = 43 →
  10. 10.4x + 5y = 11 and 2x + 3y = 5 →
  11. 11.5x + 6y = 10 and 3x + y = −7 →
  12. 12.8x + 9y = 65 and 9x + 8y = 54 →
  13. 13.6x + y = −3 and 3x + 4y = −33 →
  14. 14.7x + 3y = 6 and 3x + 7y = −26 →
  15. 15.2x + 2y = 18 and 6x + y = 29 →
  16. 16.5x + y = 39 and x + 5y = 27 →
  17. 17.x + 4y = 11 and 5x − 3y = 32 →
  18. 18.9x + 4y = 51 and 4x + 9y = 1 →
  19. 19.4x − 6y = −2 and 2x − y = −11 →
  20. 20.x + 4y = −7 and 4x + y = −13 →
  21. 21.x + 4y = 14 and x − 2y = −10 →
  22. 22.x − y = −12 and 2x − 3y = −30 →
  23. 23.2x + 5y = 42 and 5x + 2y = 21 →
  24. 24.x − 6y = −17 and 2x + 4y = −2 →
  25. 25.6x + 2y = 16 and x + 2y = −9 →
  26. 26.9x + 5y = 62 and 5x + 9y = 22 →
  27. 27.8x + y = 26 and x + 8y = 19 →
  28. 28.7x + 8y = 44 and 8x + 7y = 31 →
  29. 29.2x − 6y = −6 and 3x + 3y = 15 →
  30. 30.9x + 3y = 36 and 3x + 9y = 60 →
  31. 31.6x + 2y = −58 and 2x + y = −20 →
  32. 32.x + y = 6 and 2x + y = 7 →
  33. 33.4x + y = 32 and 2x − 3y = 30 →
  34. 34.6x + 3y = −30 and 6x + y = −42 →
  35. 35.8x + 5y = −47 and 5x + 8y = −44 →
  36. 36.3x + 3y = 9 and x − 3y = −21 →
  37. 37.5x − 5y = 55 and 4x + 5y = −1 →
  38. 38.x + 6y = 5 and 6x + y = −5 →
  39. 39.x + 3y = −29 and 3x + 2y = −38 →
  40. 40.2x + 7y = −12 and 7x + 2y = 3 →

Answer key

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

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