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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 609 · 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. 1.9x + 2y = 67 and 2x + 9y = 32 →
  2. 2.4x + 5y = −39 and 2x + 5y = −37 →
  3. 3.x + 2y = −15 and 3x + 3y = −36 →
  4. 4.4x + 6y = 26 and 2x + 5y = 23 →
  5. 5.7x + 9y = 100 and 9x + 7y = 92 →
  6. 6.3x + 4y = −4 and 6x + 3y = −33 →
  7. 7.2x + y = 2 and 6x + y = −6 →
  8. 8.x + 3y = −5 and 3x + y = 1 →
  9. 9.x + 4y = 11 and 3x + y = 22 →
  10. 10.3x + 5y = −18 and 4x − 5y = 81 →
  11. 11.2x − 5y = −11 and 5x − 5y = 10 →
  12. 12.5x + 6y = 29 and 5x + 5y = 25 →
  13. 13.2x + y = 9 and 2x + 6y = 4 →
  14. 14.x − 6y = 3 and 5x + 3y = −18 →
  15. 15.6x + 2y = 68 and 6x + 5y = 89 →
  16. 16.4x + y = 25 and 3x + 6y = 24 →
  17. 17.2x + 2y = −16 and 5x − y = −22 →
  18. 18.2x − 2y = 4 and 3x + 3y = 48 →
  19. 19.7x + 3y = 67 and 3x + 7y = 63 →
  20. 20.4x − 6y = −14 and 2x − 4y = −12 →
  21. 21.9x + 8y = −44 and 8x + 9y = −41 →
  22. 22.5x + 2y = 0 and 3x + 6y = −24 →
  23. 23.9x + y = −64 and x + 9y = 64 →
  24. 24.4x + 4y = 36 and 6x + 5y = 49 →
  25. 25.6x + 5y = −9 and 5x + 2y = −14 →
  26. 26.5x − 2y = −3 and 6x + 2y = −30 →
  27. 27.6x − 5y = 47 and x + 2y = −12 →
  28. 28.x + 3y = −18 and 4x + 5y = −9 →
  29. 29.4x − y = −30 and 4x + 4y = 0 →
  30. 30.3x + 4y = 44 and x − 3y = −20 →
  31. 31.x − 4y = 39 and 6x − 4y = 54 →
  32. 32.3x + y = −19 and x + 3y = −17 →
  33. 33.x + 8y = −68 and 8x + y = 23 →
  34. 34.6x + 6y = 18 and x − 3y = −5 →
  35. 35.4x − 3y = 9 and 4x + 2y = 14 →
  36. 36.4x + 9y = 20 and 9x + 4y = −20 →
  37. 37.2x − 2y = 10 and 4x − 3y = 21 →
  38. 38.4x + 5y = 41 and 6x + y = 29 →
  39. 39.2x − 2y = 4 and x − 4y = −13 →
  40. 40.5x + 6y = 39 and 6x + 5y = 38 →

Answer key

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

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