← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 161 · 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. 1.5x + 6y = 13 and 6x + 5y = 9 →
  2. 2.4x − y = −8 and 5x − 3y = 4 →
  3. 3.4x + 6y = −2 and 6x + 4y = −8 →
  4. 4.5x + 2y = −23 and 4x − 4y = 32 →
  5. 5.3x − 2y = 8 and 5x + y = 22 →
  6. 6.6x + y = 12 and x + 6y = 37 →
  7. 7.x + 5y = 19 and x + 3y = 9 →
  8. 8.4x − y = 5 and 6x + 5y = 53 →
  9. 9.7x + 2y = 52 and 2x + 7y = 47 →
  10. 10.x + 2y = 8 and 3x + y = 9 →
  11. 11.4x + 5y = −63 and 5x + y = −42 →
  12. 12.6x + y = −1 and x − 4y = −21 →
  13. 13.4x − y = 21 and 6x − 6y = 54 →
  14. 14.x + 6y = −45 and 6x + y = 10 →
  15. 15.3x + y = 17 and 6x + 6y = 42 →
  16. 16.5x − 4y = −7 and 2x + 3y = 34 →
  17. 17.5x + 2y = 15 and 2x + 5y = −15 →
  18. 18.4x + 2y = 14 and 2x + 4y = −8 →
  19. 19.4x + 4y = 16 and x − 4y = 14 →
  20. 20.6x + 9y = −60 and 9x + 6y = −75 →
  21. 21.3x + 6y = 42 and 4x − 3y = 12 →
  22. 22.4x + y = 29 and 6x − 3y = 3 →
  23. 23.3x + 2y = −3 and 4x + 6y = −14 →
  24. 24.x − y = 16 and x − 4y = 37 →
  25. 25.x + 3y = 28 and x + 2y = 20 →
  26. 26.6x + 9y = 75 and 9x + 6y = 75 →
  27. 27.3x − 2y = 12 and 3x + 3y = −33 →
  28. 28.4x − y = 13 and 5x + 3y = 46 →
  29. 29.7x + 2y = 60 and 2x + 7y = 30 →
  30. 30.5x + 2y = 24 and 2x + 6y = 20 →
  31. 31.x + 4y = 27 and 5x − y = −54 →
  32. 32.x + 4y = 10 and 4x + y = 10 →
  33. 33.6x − y = 22 and 5x + 2y = 24 →
  34. 34.3x − 2y = −9 and 2x + 6y = 38 →
  35. 35.5x + 3y = 13 and 3x + 6y = 12 →
  36. 36.7x + y = 13 and x + 7y = −53 →
  37. 37.4x + 3y = 43 and 2x − 3y = −19 →
  38. 38.5x + 7y = 63 and 7x + 5y = 69 →
  39. 39.7x + 4y = 36 and 4x + 7y = 30 →
  40. 40.9x + 4y = −38 and 4x + 9y = 12 →

Answer key

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

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