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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 119 · 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. 1.7x + 9y = −4 and 9x + 7y = 4 →
  2. 2.8x + 4y = 44 and 4x + 8y = 76 →
  3. 3.6x + 8y = −58 and 8x + 6y = −68 →
  4. 4.2x + 5y = 19 and 5x + 2y = −26 →
  5. 5.9x + 5y = 126 and 5x + 9y = 126 →
  6. 6.6x + 9y = 72 and 9x + 6y = 63 →
  7. 7.7x + 3y = 20 and 3x + 7y = 20 →
  8. 8.4x − 6y = −2 and 2x + 4y = 20 →
  9. 9.5x + 6y = −53 and x + 5y = −41 →
  10. 10.6x + 5y = −66 and 3x + 5y = −48 →
  11. 11.5x − 5y = 60 and 2x + 3y = 9 →
  12. 12.4x − 4y = 16 and x + 2y = −2 →
  13. 13.5x − y = −3 and 6x + y = 14 →
  14. 14.4x − 4y = −16 and 6x + y = 11 →
  15. 15.6x + 5y = 69 and 2x + 5y = 33 →
  16. 16.6x − 2y = −26 and 3x + 6y = 15 →
  17. 17.2x − 5y = 46 and x + 3y = −10 →
  18. 18.2x − 2y = 16 and 4x + 4y = 24 →
  19. 19.6x + 8y = 118 and 8x + 6y = 120 →
  20. 20.3x + 4y = 8 and 3x + 3y = 3 →
  21. 21.4x + 3y = 5 and 3x + 5y = −21 →
  22. 22.2x + y = 23 and 5x + 2y = 55 →
  23. 23.3x − 5y = −16 and x + y = 0 →
  24. 24.5x − 3y = −42 and 6x − 3y = −51 →
  25. 25.x + 2y = 1 and 2x − 4y = 18 →
  26. 26.7x + 5y = 48 and 5x + 7y = 48 →
  27. 27.5x + 4y = 21 and 4x + 5y = 24 →
  28. 28.6x + 7y = 3 and 7x + 6y = −3 →
  29. 29.3x + 2y = 16 and 2x + 3y = 19 →
  30. 30.5x − 2y = 36 and 4x − 2y = 28 →
  31. 31.8x + y = −33 and x + 8y = 51 →
  32. 32.4x + 6y = 78 and x + 3y = 33 →
  33. 33.6x + 7y = 76 and 7x + 6y = 80 →
  34. 34.2x + y = −12 and 4x + 3y = −18 →
  35. 35.2x + 7y = −1 and 7x + 2y = 19 →
  36. 36.4x − 4y = −32 and 6x + y = −13 →
  37. 37.8x + 3y = 20 and 3x + 8y = 35 →
  38. 38.2x + 7y = 30 and 7x + 2y = 15 →
  39. 39.2x + 9y = −67 and 9x + 2y = 45 →
  40. 40.6x + 2y = 8 and 5x + 6y = −15 →

Answer key

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

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