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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 375 · 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. 1.8x + 6y = 34 and 6x + 8y = 8 →
  2. 2.6x + 3y = 39 and 2x + 5y = 17 →
  3. 3.4x + 2y = −18 and x + 2y = −12 →
  4. 4.5x + y = 24 and x + 5y = 24 →
  5. 5.2x + 4y = 26 and 4x + 2y = 28 →
  6. 6.6x + 6y = 24 and 2x + 5y = 17 →
  7. 7.5x − 5y = −35 and x + 6y = 28 →
  8. 8.6x + 6y = 96 and 3x − y = 16 →
  9. 9.5x − 2y = 13 and 6x + 5y = 23 →
  10. 10.2x − 4y = 0 and 5x − 2y = −8 →
  11. 11.5x − y = −33 and x − 5y = 27 →
  12. 12.2x + 5y = −2 and 6x + 4y = −28 →
  13. 13.5x + y = 4 and x + 5y = −4 →
  14. 14.3x − 5y = −31 and 5x + 3y = −29 →
  15. 15.6x + y = 35 and x + 6y = 0 →
  16. 16.6x + 3y = −39 and 3x − y = −22 →
  17. 17.4x + y = 22 and 3x + 3y = 12 →
  18. 18.4x + 5y = 42 and 4x + y = 18 →
  19. 19.9x + 8y = −25 and 8x + 9y = −9 →
  20. 20.x − 5y = −12 and 5x − y = 12 →
  21. 21.7x + 8y = 21 and 8x + 7y = 9 →
  22. 22.9x + 5y = −76 and 5x + 9y = −36 →
  23. 23.2x + 6y = 48 and 2x − 2y = −24 →
  24. 24.3x + 4y = 30 and 4x + 3y = 33 →
  25. 25.2x + 6y = 30 and 6x + 2y = −38 →
  26. 26.5x + 7y = −5 and 7x + 5y = −31 →
  27. 27.4x − 5y = −14 and 6x + 3y = 0 →
  28. 28.5x − y = 9 and x + y = −3 →
  29. 29.4x − 2y = −2 and 5x + 5y = 50 →
  30. 30.x + 8y = −13 and 8x + y = −41 →
  31. 31.4x + y = −18 and 5x − 5y = −35 →
  32. 32.6x + 2y = 0 and 3x + 4y = −27 →
  33. 33.4x + 7y = 57 and 7x + 4y = 42 →
  34. 34.2x + 2y = 14 and x − 3y = −13 →
  35. 35.5x + 5y = 50 and 4x + 5y = 49 →
  36. 36.6x + 2y = 72 and 2x + 6y = 72 →
  37. 37.3x + 2y = 0 and 2x + 3y = −10 →
  38. 38.5x + 3y = −47 and 3x + 5y = −41 →
  39. 39.6x + 7y = 85 and 7x + 6y = 84 →
  40. 40.5x + y = −33 and x + 2y = −12 →

Answer key

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

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