← Simultaneous equations lesson New set →

Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 712 · 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. 1.6x + y = 43 and 6x − 6y = 36 →
  2. 2.4x + 2y = 26 and x + 2y = 8 →
  3. 3.7x + 3y = 31 and 3x + 7y = −21 →
  4. 4.x + 9y = 80 and 9x + y = 80 →
  5. 5.x − 6y = −31 and 2x − y = 4 →
  6. 6.3x − 3y = 18 and 4x + 2y = 42 →
  7. 7.2x − 2y = −24 and 3x + 5y = 28 →
  8. 8.6x + 6y = 36 and x − 4y = −14 →
  9. 9.2x + 3y = 20 and 6x − y = 40 →
  10. 10.4x + 6y = −38 and 4x − 6y = 22 →
  11. 11.3x + 6y = 54 and 2x + 5y = 43 →
  12. 12.3x − 2y = 25 and 2x + 4y = 6 →
  13. 13.3x + 4y = −20 and 4x + 3y = −29 →
  14. 14.3x + y = 18 and 6x + 3y = 33 →
  15. 15.x + y = −4 and 4x − y = 19 →
  16. 16.7x + 4y = 58 and 4x + 7y = 52 →
  17. 17.6x + y = 28 and 3x + y = 16 →
  18. 18.6x + y = 21 and 2x − 4y = −6 →
  19. 19.3x − 4y = −47 and 3x + 6y = 3 →
  20. 20.2x − y = 2 and 6x − y = 10 →
  21. 21.6x + y = 3 and x + 6y = −17 →
  22. 22.5x + 5y = 20 and 6x − 4y = −36 →
  23. 23.4x − 6y = −10 and 6x − 5y = −3 →
  24. 24.8x + 7y = 87 and 7x + 8y = 93 →
  25. 25.5x − y = −17 and 4x + 3y = −6 →
  26. 26.x + 6y = −11 and 6x − y = 8 →
  27. 27.3x + y = 9 and 3x + 2y = 3 →
  28. 28.3x + 3y = 33 and x + 5y = 43 →
  29. 29.3x + 5y = −17 and 5x + 3y = 9 →
  30. 30.3x + 2y = 15 and 6x + y = 39 →
  31. 31.x + 6y = −14 and 3x − 5y = −19 →
  32. 32.8x + 6y = 34 and 6x + 8y = 50 →
  33. 33.5x + 2y = −43 and 2x + 5y = −34 →
  34. 34.5x − 2y = 7 and 6x + y = 5 →
  35. 35.8x + y = −7 and x + 8y = 70 →
  36. 36.4x + 6y = 30 and 3x + 2y = 15 →
  37. 37.6x − 3y = 57 and 5x − 4y = 61 →
  38. 38.2x + 3y = 33 and 4x − 5y = −33 →
  39. 39.3x − 2y = 2 and 2x + 5y = 33 →
  40. 40.2x + 5y = 48 and 6x + 3y = 72 →

Answer key

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

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