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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 55 · 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 + 2y = 1 and 3x − 5y = −19 →
  2. 2.x + 8y = −79 and 8x + y = −65 →
  3. 3.3x + 2y = 32 and x + 4y = 24 →
  4. 4.6x − 3y = −9 and 2x + 4y = 42 →
  5. 5.5x + y = 35 and x + 5y = 31 →
  6. 6.2x + 4y = −12 and 6x + 5y = −8 →
  7. 7.6x + 5y = −4 and 6x + y = 4 →
  8. 8.5x + 5y = 70 and 6x + 3y = 66 →
  9. 9.3x + 5y = 37 and 2x − 5y = −42 →
  10. 10.5x + 4y = 42 and 6x + 6y = 54 →
  11. 11.x + 6y = −27 and 6x − y = −51 →
  12. 12.6x − 2y = 36 and 5x − 3y = 22 →
  13. 13.2x + 3y = −6 and 5x + 2y = 7 →
  14. 14.3x + 2y = −9 and x + 2y = −7 →
  15. 15.4x + 5y = 65 and 4x − y = 11 →
  16. 16.2x + 3y = −1 and 2x + 6y = −10 →
  17. 17.4x + 6y = −20 and x + 5y = −26 →
  18. 18.x − y = 2 and 2x + 5y = 32 →
  19. 19.9x + y = 64 and x + 9y = −64 →
  20. 20.4x − y = −13 and 6x + 6y = 48 →
  21. 21.3x + 5y = 2 and x + 6y = −8 →
  22. 22.6x − y = −52 and 5x + 3y = −28 →
  23. 23.4x + 3y = −60 and 3x + 4y = −59 →
  24. 24.4x + 4y = 28 and 2x + 6y = 38 →
  25. 25.9x + 8y = 64 and 8x + 9y = 55 →
  26. 26.7x + 2y = 26 and 2x + 7y = 1 →
  27. 27.3x − 6y = −39 and 2x + 3y = 16 →
  28. 28.3x + 4y = 24 and 2x − 4y = −4 →
  29. 29.3x + 4y = 13 and 4x + 5y = 18 →
  30. 30.3x + 4y = 22 and 3x + 2y = 14 →
  31. 31.3x + y = 15 and x + 2y = −5 →
  32. 32.6x + 4y = −64 and 2x + 4y = −32 →
  33. 33.2x − 2y = 36 and x − 5y = 54 →
  34. 34.6x + 2y = 4 and 6x − 4y = 10 →
  35. 35.6x + 2y = 8 and 2x + 6y = 8 →
  36. 36.3x − 4y = 11 and 6x − 5y = 25 →
  37. 37.7x + 4y = 73 and 4x + 7y = 70 →
  38. 38.2x + y = −15 and 3x + 5y = −19 →
  39. 39.7x + 8y = 85 and 8x + 7y = 80 →
  40. 40.6x − 6y = −54 and 3x − 5y = −33 →

Answer key

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

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