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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 28 · 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 − 3y = −9 and x + 2y = 16 →
  2. 2.7x + 6y = 0 and 6x + 7y = 13 →
  3. 3.5x + y = −18 and x + 5y = 6 →
  4. 4.x − 3y = 11 and 2x + 3y = −14 →
  5. 5.x + 5y = 34 and 5x + y = 2 →
  6. 6.5x + 4y = 69 and 4x + 5y = 66 →
  7. 7.8x + 6y = 108 and 6x + 8y = 102 →
  8. 8.x + 6y = −26 and 3x + 2y = −14 →
  9. 9.3x + 6y = −3 and 5x + 6y = 7 →
  10. 10.3x + 4y = −7 and x − y = −7 →
  11. 11.2x + 2y = −2 and x − 3y = −5 →
  12. 12.x + 9y = −14 and 9x + y = 34 →
  13. 13.x + y = −1 and x − y = 3 →
  14. 14.x − 4y = 9 and x + y = −1 →
  15. 15.5x + 4y = −29 and 4x + 5y = −16 →
  16. 16.5x + 9y = 26 and 9x + 5y = 58 →
  17. 17.x − y = −1 and x − 5y = −33 →
  18. 18.5x + 6y = 34 and 6x + 5y = 32 →
  19. 19.2x + 3y = 7 and 3x + 2y = 8 →
  20. 20.5x − y = −35 and 5x + 5y = −5 →
  21. 21.x + 3y = −15 and 3x + y = 11 →
  22. 22.6x + 2y = 30 and 5x − 6y = 48 →
  23. 23.8x + 2y = −52 and 2x + 8y = 32 →
  24. 24.2x − 6y = 22 and x + y = −5 →
  25. 25.7x + y = 8 and x + 7y = 8 →
  26. 26.x + 4y = −9 and 4x + 6y = −16 →
  27. 27.7x + y = 28 and x + 7y = −44 →
  28. 28.9x + 4y = 105 and 4x + 9y = 90 →
  29. 29.3x + 9y = 57 and 9x + 3y = −21 →
  30. 30.8x + 4y = 36 and 4x + 8y = −12 →
  31. 31.5x + 2y = −32 and 2x + 5y = −38 →
  32. 32.6x + 7y = 22 and 7x + 6y = 30 →
  33. 33.2x + 3y = 14 and 5x + 2y = 13 →
  34. 34.4x − y = 0 and 3x + 4y = −38 →
  35. 35.2x − 4y = 46 and 2x + 5y = −35 →
  36. 36.3x − 4y = −54 and 3x − 3y = −45 →
  37. 37.5x − 3y = 11 and 4x − 2y = 10 →
  38. 38.3x + 5y = 48 and x + y = 10 →
  39. 39.5x + 2y = 26 and 6x + 2y = 34 →
  40. 40.2x + 9y = −43 and 9x + 2y = −1 →

Answer key

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

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