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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 351 · 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 + 4y = 0 and 6x + 6y = −36 →
  2. 2.2x − 2y = 2 and 2x + y = 5 →
  3. 3.4x − 2y = 6 and 2x + y = 13 →
  4. 4.2x + 3y = 17 and 6x − 6y = 6 →
  5. 5.3x + y = −1 and 2x + 5y = −18 →
  6. 6.7x + y = 0 and x + 7y = 48 →
  7. 7.x + 4y = −10 and 5x + 6y = 6 →
  8. 8.2x + 2y = −2 and x − 6y = −8 →
  9. 9.5x − 6y = −19 and 3x + y = 7 →
  10. 10.5x + y = 31 and 3x + 2y = 20 →
  11. 11.4x + 3y = −13 and 3x + 4y = −22 →
  12. 12.4x − 2y = −16 and 3x + 5y = 1 →
  13. 13.3x − y = 27 and x + 6y = −10 →
  14. 14.3x + y = 21 and 4x + 6y = 0 →
  15. 15.5x − 2y = −27 and 2x + 4y = −54 →
  16. 16.4x + 2y = 40 and 6x − 4y = 18 →
  17. 17.3x − 2y = 14 and 6x − 2y = 32 →
  18. 18.5x + 6y = −12 and 6x + 5y = −21 →
  19. 19.4x + 3y = 31 and 3x + 4y = 39 →
  20. 20.3x + y = 27 and 3x − 6y = 6 →
  21. 21.x + y = 10 and 4x − y = 5 →
  22. 22.4x + 2y = 32 and 2x + 4y = 34 →
  23. 23.7x + 3y = −37 and 3x + 7y = −33 →
  24. 24.x − 2y = 10 and 3x − 3y = 18 →
  25. 25.2x + 4y = −4 and 4x + 2y = −20 →
  26. 26.x − 2y = −10 and 5x − 5y = −30 →
  27. 27.7x + 2y = 27 and 2x + 7y = 27 →
  28. 28.9x + 3y = −42 and 3x + 9y = −78 →
  29. 29.3x + 2y = −31 and 2x + 3y = −24 →
  30. 30.5x + 5y = 10 and 2x − 5y = −3 →
  31. 31.2x + 3y = 15 and x + 5y = 18 →
  32. 32.x + y = 8 and 2x + y = 11 →
  33. 33.5x − 4y = 48 and 6x − 2y = 52 →
  34. 34.2x + 3y = 1 and x + 5y = 18 →
  35. 35.5x + 2y = −38 and 2x + 6y = −62 →
  36. 36.x − 5y = −13 and 2x − 5y = −11 →
  37. 37.2x + 3y = 7 and 4x − 3y = 5 →
  38. 38.x + 2y = −13 and 5x − 2y = −17 →
  39. 39.6x + 2y = 58 and 2x + 6y = 30 →
  40. 40.x + y = −2 and 2x + y = −8 →

Answer key

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

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