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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 223 · 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 − 3y = 7 and 5x + 3y = 28 →
  2. 2.3x − 2y = −1 and 2x + y = 18 →
  3. 3.7x + 8y = −81 and 8x + 7y = −84 →
  4. 4.x + y = −1 and 3x + 6y = 0 →
  5. 5.2x + y = 13 and 6x + 4y = 40 →
  6. 6.x + y = 11 and 2x + 4y = 38 →
  7. 7.9x + 5y = 92 and 5x + 9y = 76 →
  8. 8.x − 2y = 13 and 3x + 2y = −1 →
  9. 9.x + 4y = −24 and 2x + 5y = −27 →
  10. 10.4x + 6y = −24 and x − y = −1 →
  11. 11.6x + 9y = 93 and 9x + 6y = 102 →
  12. 12.9x + 2y = 47 and 2x + 9y = 19 →
  13. 13.x + 3y = 13 and 3x + y = 15 →
  14. 14.x + 8y = −37 and 8x + y = 19 →
  15. 15.5x + y = −40 and 3x − 6y = −57 →
  16. 16.4x − 4y = −12 and 5x + 2y = −36 →
  17. 17.4x − 5y = −22 and x + 5y = 7 →
  18. 18.6x − 2y = −40 and 5x + 3y = −10 →
  19. 19.6x − y = 16 and 4x + 6y = −16 →
  20. 20.6x + 2y = 10 and 5x − 4y = 14 →
  21. 21.3x + 3y = 12 and 2x − 5y = −55 →
  22. 22.4x + 2y = −8 and 2x + 4y = 14 →
  23. 23.4x − y = −41 and 2x − 6y = −48 →
  24. 24.2x + 4y = 10 and 2x + y = 1 →
  25. 25.6x + 7y = −92 and 7x + 6y = −90 →
  26. 26.x − 4y = 4 and x − 5y = 3 →
  27. 27.5x + 2y = −18 and 5x + y = −19 →
  28. 28.4x + 5y = 43 and 6x + 2y = 26 →
  29. 29.6x + 4y = −58 and 4x + 6y = −42 →
  30. 30.3x + 2y = −21 and 2x + 3y = −9 →
  31. 31.2x + y = −2 and x + 2y = −13 →
  32. 32.6x + 3y = 21 and 6x − y = 25 →
  33. 33.x − 6y = −29 and 5x + y = −21 →
  34. 34.x − 6y = 20 and x − y = 0 →
  35. 35.6x + 3y = 0 and x − 6y = 13 →
  36. 36.5x + 5y = 45 and 5x + y = 25 →
  37. 37.4x + 6y = 38 and 4x + 2y = 26 →
  38. 38.4x − 2y = −4 and 6x + 3y = −42 →
  39. 39.9x + 3y = −27 and 3x + 9y = 15 →
  40. 40.6x + y = 28 and 4x + 2y = 8 →

Answer key

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

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