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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 453 · 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 + 5y = −55 and 6x − 5y = −33 →
  2. 2.6x + 3y = −51 and 5x − 2y = −47 →
  3. 3.x + 7y = −27 and 7x + y = −45 →
  4. 4.6x + 2y = 0 and 2x + 6y = 48 →
  5. 5.5x + 3y = 34 and x + 5y = 20 →
  6. 6.5x + 3y = −41 and 2x + 2y = −18 →
  7. 7.x + 2y = −11 and 2x − y = −12 →
  8. 8.5x + 3y = 14 and 2x + 3y = 11 →
  9. 9.3x + 5y = 23 and 5x + 3y = 17 →
  10. 10.2x − 4y = 14 and 5x + 5y = 5 →
  11. 11.8x + 9y = 95 and 9x + 8y = 92 →
  12. 12.2x − 4y = 6 and 4x − 4y = 16 →
  13. 13.9x + 5y = 58 and 5x + 9y = 82 →
  14. 14.2x + 6y = −28 and 3x + y = 6 →
  15. 15.2x + 6y = 28 and 4x − y = 17 →
  16. 16.4x − 2y = 40 and x + 3y = 3 →
  17. 17.8x + 9y = 79 and 9x + 8y = 74 →
  18. 18.2x − 3y = 13 and 3x + y = 3 →
  19. 19.8x + 2y = 68 and 2x + 8y = 32 →
  20. 20.x + 5y = −47 and 5x + y = −43 →
  21. 21.4x + 2y = 30 and 2x + 6y = 30 →
  22. 22.x − 5y = −19 and 3x + 6y = 48 →
  23. 23.4x + 4y = −8 and 6x + y = 23 →
  24. 24.3x + 4y = 17 and 4x + 3y = 18 →
  25. 25.x + 5y = 11 and 4x + y = 6 →
  26. 26.3x − 6y = 0 and 5x + 5y = 15 →
  27. 27.3x + 6y = 12 and 2x − 4y = 0 →
  28. 28.x + 8y = 23 and 8x + y = −68 →
  29. 29.x + 9y = 23 and 9x + y = 47 →
  30. 30.4x + 2y = 0 and 6x − y = 16 →
  31. 31.5x − 2y = 36 and 4x − 2y = 32 →
  32. 32.4x + 3y = −43 and 4x − 2y = 2 →
  33. 33.2x − y = −3 and 6x + y = −21 →
  34. 34.6x + y = 22 and x − 3y = 10 →
  35. 35.6x + 6y = 24 and 6x + 3y = 33 →
  36. 36.6x − 3y = −33 and 6x + 4y = 2 →
  37. 37.3x + y = 12 and x + y = 6 →
  38. 38.5x + 6y = 21 and x − 5y = 29 →
  39. 39.4x − y = 13 and 2x + 3y = 31 →
  40. 40.9x + 2y = 1 and 2x + 9y = 43 →

Answer key

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

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