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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 263 · 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.x + 8y = −69 and 8x + y = −48 →
  2. 2.6x − 5y = 16 and x − 2y = −2 →
  3. 3.x + y = 6 and 2x + 6y = 8 →
  4. 4.6x + y = −43 and 4x + 3y = −45 →
  5. 5.x + 9y = 49 and 9x + y = 41 →
  6. 6.7x + 2y = 41 and 2x + 7y = −14 →
  7. 7.4x + y = 37 and 5x − 4y = 20 →
  8. 8.6x + 2y = 42 and 2x + y = 16 →
  9. 9.2x + 3y = 12 and 4x − 2y = 8 →
  10. 10.6x − 4y = 16 and 2x − 2y = 4 →
  11. 11.7x + 3y = −32 and 3x + 7y = −8 →
  12. 12.6x − y = 45 and 2x + 3y = 5 →
  13. 13.5x + 3y = −9 and x + y = −1 →
  14. 14.5x + y = −1 and x + 5y = −29 →
  15. 15.9x + 3y = −18 and 3x + 9y = 18 →
  16. 16.3x − y = 22 and 3x + y = 20 →
  17. 17.4x + 5y = −21 and 3x + 4y = −18 →
  18. 18.2x − 6y = −70 and 6x + 6y = 6 →
  19. 19.x + 4y = 13 and 4x + y = −8 →
  20. 20.x + 2y = −10 and 3x + 3y = −12 →
  21. 21.5x + 2y = −43 and 4x + 4y = −32 →
  22. 22.2x + 3y = 5 and 3x − 5y = −2 →
  23. 23.4x + 6y = 20 and 6x + 4y = 0 →
  24. 24.2x − 2y = −22 and 6x + 4y = 14 →
  25. 25.9x + 7y = 30 and 7x + 9y = 34 →
  26. 26.5x + 2y = 37 and 2x + 5y = 40 →
  27. 27.6x + 6y = 42 and 3x + 4y = 25 →
  28. 28.2x + 5y = 7 and 4x − 5y = −1 →
  29. 29.3x + 6y = −33 and 6x + 3y = −12 →
  30. 30.6x − 6y = −6 and 3x − y = 5 →
  31. 31.2x + 8y = 18 and 8x + 2y = 42 →
  32. 32.5x − y = −41 and 2x + 2y = −2 →
  33. 33.x + y = 16 and 6x + 5y = 88 →
  34. 34.x + 2y = 15 and 3x + 2y = 9 →
  35. 35.x − 5y = −7 and 6x + 3y = 57 →
  36. 36.2x + 4y = 14 and 6x + 3y = −12 →
  37. 37.x − 4y = −15 and 3x + 4y = 19 →
  38. 38.3x + 4y = 11 and 4x + 5y = 14 →
  39. 39.5x + 3y = −26 and 4x − 6y = 38 →
  40. 40.4x + 2y = 30 and 3x + 3y = 36 →

Answer key

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

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