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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 278 · 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 = 18 and x + 2y = 18 →
  2. 2.x + y = −7 and x − 2y = 8 →
  3. 3.4x + 6y = 38 and 6x + 4y = 32 →
  4. 4.4x + y = −1 and x + 4y = −34 →
  5. 5.5x − 2y = −61 and x + 5y = 31 →
  6. 6.5x + 2y = 19 and 5x + 5y = 40 →
  7. 7.6x + 2y = −16 and 5x + 6y = −9 →
  8. 8.3x + 2y = −35 and 2x + y = −21 →
  9. 9.2x + 8y = 34 and 8x + 2y = −14 →
  10. 10.4x + 2y = 2 and 5x − 6y = 79 →
  11. 11.x − 4y = 40 and 4x − 6y = 70 →
  12. 12.8x + 4y = 4 and 4x + 8y = −16 →
  13. 13.5x + 6y = 19 and 6x + 5y = 3 →
  14. 14.3x + 5y = 7 and 5x + 3y = 17 →
  15. 15.8x + 7y = −8 and 7x + 8y = −22 →
  16. 16.4x + 5y = −21 and x + 3y = −14 →
  17. 17.4x + 4y = −8 and 6x + 2y = −32 →
  18. 18.4x + 3y = −4 and 3x + y = 2 →
  19. 19.6x + 6y = 0 and 2x − 4y = −42 →
  20. 20.2x + y = −6 and 2x − 2y = 0 →
  21. 21.3x − 6y = −9 and 3x − 5y = −11 →
  22. 22.5x + 5y = 45 and 4x − 4y = 12 →
  23. 23.2x + 6y = 34 and 4x + 5y = 33 →
  24. 24.4x + 8y = 108 and 8x + 4y = 108 →
  25. 25.x + 3y = 19 and 3x + 3y = 33 →
  26. 26.2x − 5y = 17 and x + 6y = −34 →
  27. 27.6x − 4y = 6 and 2x − 4y = −14 →
  28. 28.5x + 2y = 9 and 4x − y = 2 →
  29. 29.3x + y = −3 and 2x − 2y = 22 →
  30. 30.4x + 7y = 69 and 7x + 4y = 63 →
  31. 31.3x + 5y = 18 and 5x + y = 8 →
  32. 32.4x + 2y = 20 and 4x + y = 18 →
  33. 33.6x − 2y = −40 and 6x + 3y = −60 →
  34. 34.9x + 8y = −113 and 8x + 9y = −108 →
  35. 35.3x + 5y = −39 and 4x − 5y = 53 →
  36. 36.4x − 6y = 12 and 6x + 2y = 40 →
  37. 37.4x + 6y = −12 and 3x + 2y = 11 →
  38. 38.3x + 5y = 43 and 5x + y = 35 →
  39. 39.2x + y = −4 and 5x + 3y = −8 →
  40. 40.x + 8y = 35 and 8x + y = 28 →

Answer key

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

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