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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 101 · 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. 1.4x + 8y = 0 and 8x + 4y = −24 →
  2. 2.4x + 5y = 21 and 4x + 6y = 18 →
  3. 3.6x + 5y = 49 and 3x − 2y = 29 →
  4. 4.3x + 6y = −30 and 4x + 2y = −4 →
  5. 5.3x − y = −20 and 2x + 2y = −16 →
  6. 6.x + y = 4 and 5x + y = 24 →
  7. 7.3x + 6y = −27 and 4x + y = 6 →
  8. 8.x + 8y = 79 and 8x + y = 65 →
  9. 9.5x + 2y = −2 and 2x + 5y = 16 →
  10. 10.x − 2y = −12 and 3x − 2y = −28 →
  11. 11.6x + 3y = −9 and 3x + 6y = −36 →
  12. 12.x + 6y = 41 and 2x − y = 4 →
  13. 13.9x + 5y = 5 and 5x + 9y = −47 →
  14. 14.x + 4y = −26 and 3x − 5y = 41 →
  15. 15.5x − 6y = −17 and 3x − 2y = 1 →
  16. 16.x − 5y = 0 and 6x − y = 29 →
  17. 17.2x + y = −9 and 2x − 4y = −14 →
  18. 18.6x + 3y = 51 and 6x + y = 49 →
  19. 19.4x + 2y = 38 and 2x − y = 9 →
  20. 20.5x + 3y = 54 and 6x + y = 57 →
  21. 21.4x + 7y = 56 and 7x + 4y = 65 →
  22. 22.6x + 4y = −32 and 5x + y = −29 →
  23. 23.x + 5y = 40 and 4x + 3y = 7 →
  24. 24.2x + 3y = 5 and 3x − 4y = 33 →
  25. 25.6x + 3y = −42 and 2x + 3y = −26 →
  26. 26.4x + 3y = 29 and 2x − 4y = −24 →
  27. 27.x + 3y = −12 and x + 4y = −18 →
  28. 28.3x − 3y = −3 and 2x + y = −8 →
  29. 29.6x + 5y = 3 and x + 2y = −3 →
  30. 30.x − 6y = −26 and 4x + y = 21 →
  31. 31.9x + 6y = 18 and 6x + 9y = −3 →
  32. 32.2x − 6y = −10 and 5x + y = 23 →
  33. 33.7x + 9y = 121 and 9x + 7y = 119 →
  34. 34.x + 8y = −51 and 8x + y = 33 →
  35. 35.4x − 2y = 16 and x + 5y = −7 →
  36. 36.2x − 2y = −16 and 4x + 5y = −41 →
  37. 37.2x + 6y = −28 and 6x + 2y = −36 →
  38. 38.4x − 6y = 32 and 5x + 4y = −29 →
  39. 39.x + 5y = −22 and 6x + 2y = 36 →
  40. 40.6x + 4y = 54 and 4x + 6y = 46 →

Answer key

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

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