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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 531 · 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 + 6y = −28 and 6x + 5y = −38 →
  2. 2.6x + 6y = 0 and x + 3y = −2 →
  3. 3.x + 6y = 56 and 5x + 2y = 56 →
  4. 4.4x − 4y = −28 and 6x + 2y = 30 →
  5. 5.5x − 4y = −52 and 3x + 2y = −18 →
  6. 6.x + 3y = 22 and 3x − 3y = −42 →
  7. 7.3x + y = 8 and 2x + 4y = −18 →
  8. 8.9x + 3y = −42 and 3x + 9y = −54 →
  9. 9.x + 2y = 7 and 3x − 4y = 1 →
  10. 10.2x + 3y = 18 and 3x + 2y = 7 →
  11. 11.x + 5y = 30 and 3x + 3y = 6 →
  12. 12.2x + 2y = 4 and 5x + y = 18 →
  13. 13.3x + y = 14 and x + 3y = 18 →
  14. 14.3x − 5y = −29 and 3x + 6y = 48 →
  15. 15.4x − y = 22 and 5x − y = 29 →
  16. 16.3x − 6y = 33 and 5x − 2y = 7 →
  17. 17.2x + y = 10 and x + 2y = −1 →
  18. 18.x + y = −7 and x + 6y = −2 →
  19. 19.3x + 4y = 22 and 4x + 3y = 13 →
  20. 20.6x + y = 32 and x + 6y = 17 →
  21. 21.3x + 6y = 57 and 4x + 3y = 46 →
  22. 22.5x − y = 16 and 6x + 5y = 44 →
  23. 23.2x + y = 18 and 3x − y = 17 →
  24. 24.6x − 6y = −6 and 2x − 4y = −12 →
  25. 25.6x + 4y = −22 and x − 2y = −17 →
  26. 26.x + 3y = 3 and 6x − 5y = −28 →
  27. 27.6x − y = 44 and 2x + 3y = 8 →
  28. 28.5x + y = −18 and 3x − y = −22 →
  29. 29.4x + y = 0 and 4x + 2y = 8 →
  30. 30.7x + 6y = −10 and 6x + 7y = −16 →
  31. 31.6x + 4y = 18 and x + y = 1 →
  32. 32.x − 2y = −3 and 6x + y = 34 →
  33. 33.2x + 2y = −2 and 3x − y = −19 →
  34. 34.4x + 6y = −34 and 6x + 4y = −26 →
  35. 35.3x + y = 26 and 4x + y = 33 →
  36. 36.4x − 3y = −16 and 3x + 2y = 22 →
  37. 37.2x − 3y = 4 and x − 4y = −8 →
  38. 38.3x + y = −14 and 4x + y = −18 →
  39. 39.2x + 5y = 49 and 4x − 4y = −28 →
  40. 40.5x + 7y = 59 and 7x + 5y = 73 →

Answer key

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

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