← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 423 · 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 + 9y = −55 and 9x + 7y = −57 →
  2. 2.x + 9y = 8 and 9x + y = −8 →
  3. 3.4x − 5y = −32 and x + 2y = 18 →
  4. 4.x + 4y = 5 and 2x − 2y = −20 →
  5. 5.5x − 4y = −22 and 5x + y = 18 →
  6. 6.6x + 6y = 24 and 3x + 2y = 7 →
  7. 7.6x + 7y = 44 and 7x + 6y = 34 →
  8. 8.3x − 3y = 0 and x − 4y = −24 →
  9. 9.5x − 5y = −20 and x + 5y = −28 →
  10. 10.4x − 4y = 20 and 2x + 4y = 28 →
  11. 11.5x − 2y = −1 and 6x + 5y = 58 →
  12. 12.5x − 3y = −28 and x + 5y = 28 →
  13. 13.4x + 3y = −7 and 6x − 3y = −3 →
  14. 14.4x + y = 25 and 6x − 3y = −3 →
  15. 15.7x + 6y = 13 and 6x + 7y = 13 →
  16. 16.8x + 7y = 128 and 7x + 8y = 127 →
  17. 17.6x + 5y = 7 and 2x + 4y = −14 →
  18. 18.3x − 2y = −23 and 4x + 4y = −24 →
  19. 19.5x − y = 11 and x − 4y = −13 →
  20. 20.8x + y = 28 and x + 8y = 35 →
  21. 21.x + 8y = 69 and 8x + y = −15 →
  22. 22.4x + 2y = 10 and 6x + 2y = 18 →
  23. 23.x − 3y = 23 and 3x − 5y = 33 →
  24. 24.3x + 6y = 51 and 4x + y = 19 →
  25. 25.4x − 3y = −21 and 2x − 2y = −12 →
  26. 26.5x + 8y = 88 and 8x + 5y = 94 →
  27. 27.4x + 2y = −26 and 3x − 4y = 8 →
  28. 28.2x + 5y = −16 and 5x + 2y = −19 →
  29. 29.4x − 6y = −2 and 6x + 2y = −36 →
  30. 30.4x − y = 2 and 3x + 6y = −39 →
  31. 31.x + 6y = −11 and 4x + 6y = −8 →
  32. 32.x + 9y = 0 and 9x + y = 80 →
  33. 33.5x + 4y = 61 and 4x + 5y = 65 →
  34. 34.3x + 8y = 59 and 8x + 3y = 84 →
  35. 35.9x + 3y = −54 and 3x + 9y = −42 →
  36. 36.3x + 4y = −30 and 2x + 3y = −23 →
  37. 37.3x + y = −16 and 5x − 2y = −23 →
  38. 38.x + 2y = −16 and 6x + 2y = −36 →
  39. 39.2x + y = −6 and 2x + 4y = −12 →
  40. 40.6x − 5y = −37 and x + 2y = 8 →

Answer key

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

Free vedic maths lessons, practice and worksheets at talentjr.in/vedic-maths