← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 20 · 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. 1.2x + y = −10 and x + 2y = −14 →
  2. 2.4x + 5y = −36 and 5x + 4y = −27 →
  3. 3.4x + 2y = 34 and x + y = 8 →
  4. 4.4x + 2y = 22 and 2x + 4y = 32 →
  5. 5.5x + 5y = 70 and 2x − y = 1 →
  6. 6.3x + 6y = −30 and 6x − 6y = 66 →
  7. 7.x + 9y = 66 and 9x + y = 34 →
  8. 8.8x + 7y = −84 and 7x + 8y = −81 →
  9. 9.3x + 5y = −4 and 5x − 2y = −17 →
  10. 10.x + 6y = 7 and x + 2y = 3 →
  11. 11.x + 4y = 2 and 4x + y = −7 →
  12. 12.x + y = −7 and 6x + 3y = −24 →
  13. 13.2x + 3y = 10 and 6x + 5y = 22 →
  14. 14.x + 2y = 8 and 2x + y = 10 →
  15. 15.3x + 6y = 18 and 2x − 6y = −28 →
  16. 16.x + 3y = 2 and 3x + y = −18 →
  17. 17.5x + 2y = −30 and 2x + 5y = −33 →
  18. 18.x + 3y = −25 and 3x + y = −3 →
  19. 19.5x − 2y = −47 and 6x + 6y = −6 →
  20. 20.3x + 3y = 18 and 6x − 2y = 12 →
  21. 21.6x + 7y = 89 and 7x + 6y = 93 →
  22. 22.8x + y = 21 and x + 8y = −21 →
  23. 23.3x + 4y = −17 and 4x + 3y = −4 →
  24. 24.6x + 5y = −60 and 5x + 6y = −61 →
  25. 25.6x + 7y = 99 and 7x + 6y = 96 →
  26. 26.7x + 9y = −54 and 9x + 7y = −74 →
  27. 27.4x + 7y = 16 and 7x + 4y = −5 →
  28. 28.5x + 4y = 25 and 2x − 4y = 38 →
  29. 29.4x + y = 7 and 4x + 5y = 3 →
  30. 30.4x + 8y = −60 and 8x + 4y = −24 →
  31. 31.6x + 2y = −48 and 6x + y = −42 →
  32. 32.x − 5y = −6 and 6x + 4y = −2 →
  33. 33.6x + 5y = 28 and x + 2y = 14 →
  34. 34.6x − 6y = −66 and 5x + 3y = −15 →
  35. 35.4x + y = −20 and x + 4y = 10 →
  36. 36.2x − y = 5 and 2x + 6y = 40 →
  37. 37.4x + 3y = 30 and x + 2y = 15 →
  38. 38.3x + 4y = 12 and 4x + 3y = 2 →
  39. 39.6x + 2y = 38 and 3x + 5y = 35 →
  40. 40.4x + 8y = 16 and 8x + 4y = −16 →

Answer key

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

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