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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 759 · 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. 1.8x + 6y = −58 and 6x + 8y = −54 →
  2. 2.5x + 4y = 52 and x − 2y = −12 →
  3. 3.5x + 3y = 32 and 2x + 2y = 16 →
  4. 4.2x + 9y = 43 and 9x + 2y = 1 →
  5. 5.4x + 4y = 4 and x + 6y = −24 →
  6. 6.6x + 3y = −15 and 2x − 5y = 49 →
  7. 7.6x + 4y = −6 and 4x + 6y = −24 →
  8. 8.x + 9y = 55 and 9x + y = −65 →
  9. 9.5x + 6y = 5 and x − 6y = 37 →
  10. 10.8x + 7y = −19 and 7x + 8y = −26 →
  11. 11.6x − 6y = 54 and 4x + y = 31 →
  12. 12.5x + 7y = −16 and 7x + 5y = −32 →
  13. 13.x + y = −3 and 4x + 2y = −20 →
  14. 14.5x + 3y = −33 and 2x − 4y = −8 →
  15. 15.3x + 3y = 0 and 3x − 6y = −36 →
  16. 16.4x + 2y = −26 and 2x + 4y = −34 →
  17. 17.4x + 3y = −16 and 3x + 4y = −26 →
  18. 18.4x + 6y = −58 and 2x + y = −15 →
  19. 19.3x + y = 22 and 3x + 2y = 23 →
  20. 20.6x + 9y = 3 and 9x + 6y = −3 →
  21. 21.6x + 2y = 18 and 4x + y = 15 →
  22. 22.2x + 4y = −6 and 4x + 2y = 18 →
  23. 23.x + 5y = 24 and 3x + 4y = 28 →
  24. 24.2x + y = 9 and x − 6y = −15 →
  25. 25.6x + 2y = 4 and 2x − 2y = 4 →
  26. 26.9x + 7y = −47 and 7x + 9y = −33 →
  27. 27.3x + 7y = −5 and 7x + 3y = 15 →
  28. 28.5x − 3y = 19 and 4x − y = 25 →
  29. 29.5x + 6y = −7 and 6x + 5y = −4 →
  30. 30.2x + 2y = 10 and 3x + 6y = 21 →
  31. 31.6x + y = 40 and x + 6y = −40 →
  32. 32.7x + 5y = −1 and 5x + 7y = −11 →
  33. 33.9x + 2y = −37 and 2x + 9y = 26 →
  34. 34.2x − 5y = −53 and 3x + 3y = −6 →
  35. 35.6x + 5y = 51 and 6x − 3y = −21 →
  36. 36.x + 3y = −3 and 6x + 6y = 18 →
  37. 37.x + 3y = 18 and 6x + y = 23 →
  38. 38.4x − y = −8 and 6x + 6y = 18 →
  39. 39.5x + 6y = −12 and x − 4y = 34 →
  40. 40.2x + 6y = 64 and 6x + 2y = 64 →

Answer key

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

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