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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 442 · 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 + 5y = 27 and 5x + 7y = 33 →
  2. 2.5x + 4y = −42 and 5x + 5y = −50 →
  3. 3.x − y = −2 and x + 3y = 18 →
  4. 4.x + 4y = 18 and 4x + y = −3 →
  5. 5.2x + y = 6 and x + 2y = 15 →
  6. 6.2x + 5y = 58 and 3x + 5y = 67 →
  7. 7.5x + 3y = 11 and 5x − 2y = −24 →
  8. 8.3x + 4y = −20 and 2x − 5y = 48 →
  9. 9.6x + 3y = 9 and 4x − 5y = −29 →
  10. 10.7x + 6y = −3 and 6x + 7y = 3 →
  11. 11.x + y = 0 and x + 4y = 21 →
  12. 12.5x + 2y = −27 and 2x + y = −10 →
  13. 13.2x − y = 24 and 6x + 4y = 16 →
  14. 14.6x + 4y = 36 and x − 4y = −22 →
  15. 15.5x − y = 44 and x − 3y = 6 →
  16. 16.6x + 8y = 84 and 8x + 6y = 84 →
  17. 17.2x − 3y = 25 and x − 5y = 23 →
  18. 18.x + 5y = −4 and 4x − 4y = 8 →
  19. 19.3x + 4y = 6 and 4x − 3y = −17 →
  20. 20.x − 3y = 15 and 3x − 3y = 21 →
  21. 21.6x + 2y = 38 and 2x + 6y = 18 →
  22. 22.2x + 3y = 19 and x + 3y = 20 →
  23. 23.6x + 4y = 20 and 4x + 6y = 20 →
  24. 24.x + 2y = −13 and 6x − y = −13 →
  25. 25.6x − 6y = 66 and 2x + 6y = −42 →
  26. 26.6x + 3y = 36 and x + 5y = 24 →
  27. 27.x − 3y = −11 and 4x + y = 21 →
  28. 28.6x + 2y = 32 and x − y = 4 →
  29. 29.9x + y = 60 and x + 9y = 60 →
  30. 30.5x + y = 6 and 5x + 4y = −21 →
  31. 31.x + 4y = −6 and 4x + y = 6 →
  32. 32.2x − 3y = −8 and 3x + 3y = 18 →
  33. 33.6x + 5y = −8 and 5x − 5y = 30 →
  34. 34.x + 6y = 32 and 6x + y = 52 →
  35. 35.3x + 6y = 27 and 4x + 3y = 21 →
  36. 36.3x + 2y = 14 and 5x + 5y = 25 →
  37. 37.x + 3y = −6 and 6x + 5y = 16 →
  38. 38.x + 5y = 22 and 3x − 2y = −19 →
  39. 39.4x − 4y = 20 and 6x + y = −33 →
  40. 40.6x + 2y = 42 and 2x − 5y = 31 →

Answer key

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

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