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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 457 · 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 + 3y = 19 and 4x + y = 4 →
  2. 2.6x + 5y = −1 and x − 2y = −3 →
  3. 3.7x + 4y = −8 and 4x + 7y = −47 →
  4. 4.2x + 5y = 34 and x + 6y = 38 →
  5. 5.3x + 5y = 29 and 5x + 3y = 43 →
  6. 6.6x + 4y = 44 and 5x + y = 32 →
  7. 7.2x + y = −2 and 5x + 5y = 15 →
  8. 8.2x − 4y = 0 and x + 4y = 6 →
  9. 9.3x + y = −12 and 4x + 3y = −1 →
  10. 10.2x + 4y = 36 and 3x − 3y = 9 →
  11. 11.5x + y = 4 and x + 5y = −4 →
  12. 12.2x + 5y = 37 and 4x − 4y = −24 →
  13. 13.5x + 4y = 57 and 6x − 3y = 6 →
  14. 14.5x + 6y = −18 and x + 6y = 6 →
  15. 15.5x + 4y = −12 and 5x − 2y = −24 →
  16. 16.9x + 2y = 99 and 2x + 9y = 99 →
  17. 17.6x + y = 41 and x + y = 1 →
  18. 18.6x + 3y = 45 and 3x + 6y = 54 →
  19. 19.5x + 2y = −4 and 2x + 5y = −31 →
  20. 20.6x + y = −10 and 4x + 6y = 4 →
  21. 21.4x + 7y = 53 and 7x + 4y = 68 →
  22. 22.6x + 4y = −28 and 6x − 4y = −68 →
  23. 23.3x + 3y = −42 and x + 6y = −49 →
  24. 24.5x + 4y = −11 and 4x + 4y = −16 →
  25. 25.2x + 5y = −3 and 3x + y = −24 →
  26. 26.2x + 3y = 8 and x + 6y = 22 →
  27. 27.2x − 2y = −8 and 5x + y = 10 →
  28. 28.2x + 4y = 14 and 4x + 6y = 22 →
  29. 29.5x + 2y = 27 and 2x + 5y = 36 →
  30. 30.5x + 6y = 74 and 6x + 5y = 69 →
  31. 31.3x + 2y = 19 and 6x − 2y = 8 →
  32. 32.2x − 3y = −14 and 6x + 5y = 42 →
  33. 33.x + 3y = 32 and 3x + y = 24 →
  34. 34.2x + y = 20 and 4x − 4y = 28 →
  35. 35.4x + 3y = −17 and 6x + 3y = −33 →
  36. 36.7x + 4y = 63 and 4x + 7y = 69 →
  37. 37.4x + 3y = 39 and 3x + 4y = 38 →
  38. 38.5x − 5y = 0 and x + y = 6 →
  39. 39.3x + 9y = 75 and 9x + 3y = 33 →
  40. 40.5x − 4y = 5 and 6x + 3y = −33 →

Answer key

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

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