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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 619 · 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.x + 6y = −18 and 4x + 6y = −36 →
  2. 2.4x + 2y = 20 and x + 2y = 2 →
  3. 3.2x − y = 8 and 3x − y = 11 →
  4. 4.6x − y = 52 and 6x + 3y = 60 →
  5. 5.6x + 5y = 18 and 6x − 2y = 60 →
  6. 6.6x + 3y = 3 and 2x + 4y = −14 →
  7. 7.2x + 4y = 28 and 5x + 4y = 16 →
  8. 8.2x + 2y = −2 and 4x + y = 5 →
  9. 9.8x + 9y = 54 and 9x + 8y = 65 →
  10. 10.5x + 4y = 19 and 3x + 4y = 13 →
  11. 11.5x + 3y = −7 and 3x + 5y = −17 →
  12. 12.5x + 6y = 28 and 6x + 5y = 27 →
  13. 13.x − 5y = 24 and 6x + 5y = −31 →
  14. 14.6x + 6y = −36 and 4x + 2y = −26 →
  15. 15.4x + 2y = −20 and 6x − 4y = −16 →
  16. 16.4x − 6y = 74 and 2x + 5y = −19 →
  17. 17.4x − 5y = 54 and 2x + 3y = −6 →
  18. 18.2x + y = 4 and 2x − y = 0 →
  19. 19.2x − 3y = −11 and 6x − y = 23 →
  20. 20.5x + 4y = 13 and 4x + 5y = 14 →
  21. 21.4x − 5y = −36 and 5x + y = 13 →
  22. 22.4x − 5y = 28 and 4x + 4y = −8 →
  23. 23.4x + 3y = 28 and 3x + 4y = 35 →
  24. 24.3x + 2y = 2 and 6x + 5y = 8 →
  25. 25.6x + 7y = 52 and 7x + 6y = 52 →
  26. 26.5x + 4y = 11 and 6x − y = −10 →
  27. 27.3x + y = −17 and 4x + 5y = 3 →
  28. 28.3x − y = 10 and 6x + 5y = 76 →
  29. 29.4x + 5y = 33 and x + y = 8 →
  30. 30.6x + 9y = 6 and 9x + 6y = 39 →
  31. 31.2x + 3y = −20 and 3x + y = −16 →
  32. 32.7x + 6y = 55 and 6x + 7y = 62 →
  33. 33.3x − y = −11 and 2x + 2y = 14 →
  34. 34.9x + 4y = −55 and 4x + 9y = −10 →
  35. 35.2x + 7y = 75 and 7x + 2y = 60 →
  36. 36.5x + 4y = 52 and 4x + 5y = 56 →
  37. 37.3x − 6y = 6 and 5x − 5y = 15 →
  38. 38.2x + y = 17 and x + 4y = 12 →
  39. 39.x + 6y = 46 and 6x + y = −39 →
  40. 40.x + 2y = −20 and 2x + y = −16 →

Answer key

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

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