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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 694 · 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. 1.2x − y = −5 and 4x + 6y = 14 →
  2. 2.6x + 5y = 64 and 4x − 5y = 26 →
  3. 3.2x − 2y = 24 and 6x + y = 51 →
  4. 4.3x + 3y = 21 and 4x + 3y = 19 →
  5. 5.6x − 2y = 10 and 2x + 2y = 6 →
  6. 6.x + 5y = −19 and x + 3y = −11 →
  7. 7.6x + 2y = 52 and 2x + 6y = 44 →
  8. 8.2x + 3y = 35 and 3x + 2y = 35 →
  9. 9.4x + y = −33 and x − y = −12 →
  10. 10.8x + 3y = 54 and 3x + 8y = 34 →
  11. 11.5x + 7y = −9 and 7x + 5y = −3 →
  12. 12.x + 4y = −35 and 4x + 2y = −14 →
  13. 13.5x − 2y = 33 and 4x + y = 29 →
  14. 14.3x + 6y = 57 and 2x + 5y = 45 →
  15. 15.x − 2y = −1 and 6x + 6y = 66 →
  16. 16.2x + y = 23 and x + 2y = 25 →
  17. 17.2x − 5y = 7 and 4x − y = 23 →
  18. 18.6x − 5y = −58 and 2x + 5y = 34 →
  19. 19.6x + 3y = 42 and 3x + 3y = 24 →
  20. 20.4x + 8y = 4 and 8x + 4y = −52 →
  21. 21.4x + y = 17 and x + 4y = 23 →
  22. 22.2x + y = −8 and x + 2y = −7 →
  23. 23.6x − y = 26 and 6x + 6y = 12 →
  24. 24.4x + y = 27 and x + 4y = −12 →
  25. 25.5x + 3y = −2 and 6x − 5y = −11 →
  26. 26.5x + 2y = 13 and 2x + 5y = 22 →
  27. 27.5x − 6y = −38 and x + y = 10 →
  28. 28.4x + 2y = 16 and 2x + 4y = −10 →
  29. 29.2x − 4y = 6 and x + 2y = 15 →
  30. 30.9x + 7y = 26 and 7x + 9y = 6 →
  31. 31.4x + 6y = −4 and 2x − 3y = −14 →
  32. 32.2x + y = 13 and 2x − y = 23 →
  33. 33.x + 4y = 16 and 6x + 2y = −36 →
  34. 34.x + 4y = 12 and 4x + y = −12 →
  35. 35.x + 4y = −9 and 5x + y = 31 →
  36. 36.6x + 3y = 18 and 4x + y = 10 →
  37. 37.6x − 3y = 66 and x − 4y = 25 →
  38. 38.2x + 6y = 18 and 3x − 3y = 15 →
  39. 39.6x + 5y = 12 and 5x − y = 41 →
  40. 40.5x + 3y = 9 and 3x − y = −17 →

Answer key

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

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