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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 216 · 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 − 2y = 19 and 4x + 6y = 6 →
  2. 2.x − 4y = −9 and 5x + 6y = 7 →
  3. 3.2x + 3y = 22 and x + y = 9 →
  4. 4.6x + 5y = 17 and 6x + 3y = 3 →
  5. 5.6x + 5y = −4 and 6x − 3y = 60 →
  6. 6.8x + 7y = −7 and 7x + 8y = −23 →
  7. 7.2x + 4y = 26 and 6x + 6y = 42 →
  8. 8.3x + 5y = −30 and 4x − 4y = 56 →
  9. 9.6x + 9y = 45 and 9x + 6y = 45 →
  10. 10.5x + 5y = 15 and 5x + 4y = 16 →
  11. 11.2x + 5y = 33 and 5x + 3y = 35 →
  12. 12.5x + y = −36 and x + 5y = 36 →
  13. 13.4x + 4y = 52 and 2x − 2y = 2 →
  14. 14.5x − y = −37 and 6x + 4y = −34 →
  15. 15.4x + 6y = −2 and 3x − 3y = −39 →
  16. 16.8x + y = 44 and x + 8y = −26 →
  17. 17.6x + 7y = −4 and 7x + 6y = 4 →
  18. 18.4x + 7y = 44 and 7x + 4y = 44 →
  19. 19.x − 4y = −35 and 5x + 4y = −7 →
  20. 20.x + 6y = 14 and 6x + y = 14 →
  21. 21.x + 4y = −18 and 4x + y = −27 →
  22. 22.x + 2y = 15 and 3x + 4y = 39 →
  23. 23.2x + 6y = −26 and 6x + 2y = 18 →
  24. 24.2x + 5y = 26 and 2x − 3y = −22 →
  25. 25.5x + y = 28 and 3x + 6y = 60 →
  26. 26.x + 6y = −15 and 6x + y = 50 →
  27. 27.2x + 3y = 45 and x + 4y = 45 →
  28. 28.x + 4y = 30 and 4x + y = 15 →
  29. 29.2x + 6y = −22 and 6x + 2y = −34 →
  30. 30.8x + 4y = −16 and 4x + 8y = 40 →
  31. 31.3x + 5y = 69 and 6x + 3y = 75 →
  32. 32.6x − y = −17 and 3x + 4y = 14 →
  33. 33.2x + y = 8 and x + 2y = 7 →
  34. 34.5x + y = 39 and 2x + 2y = 6 →
  35. 35.4x + 8y = −8 and 8x + 4y = −28 →
  36. 36.x + 5y = 27 and 5x + y = −33 →
  37. 37.x − 5y = −31 and 5x + 2y = −20 →
  38. 38.2x + 2y = 14 and x − 2y = −20 →
  39. 39.3x + 8y = −5 and 8x + 3y = 5 →
  40. 40.9x + 6y = −60 and 6x + 9y = −30 →

Answer key

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

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