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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 755 · 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 + 4y = 9 and x + y = 6 →
  2. 2.5x + 4y = −27 and 5x + 5y = −25 →
  3. 3.5x + 9y = 68 and 9x + 5y = 44 →
  4. 4.9x + 7y = −79 and 7x + 9y = −65 →
  5. 5.2x − 2y = −8 and 2x − 3y = −10 →
  6. 6.6x + 3y = −63 and x + 2y = −21 →
  7. 7.3x − 3y = 48 and 5x + y = 32 →
  8. 8.4x + 5y = 42 and 5x + 4y = 48 →
  9. 9.4x + 3y = 19 and 6x + 6y = 24 →
  10. 10.x + 4y = −1 and 6x + 4y = 34 →
  11. 11.2x + 6y = 8 and 6x + 2y = 8 →
  12. 12.4x + 5y = 24 and 3x − 2y = −5 →
  13. 13.5x − 4y = −10 and 2x − y = −1 →
  14. 14.4x + 3y = 42 and 5x + 5y = 55 →
  15. 15.9x + 2y = 20 and 2x + 9y = 13 →
  16. 16.5x − 2y = −42 and x − 4y = −12 →
  17. 17.6x − 3y = 21 and 6x − 4y = 12 →
  18. 18.2x + 6y = 42 and 4x − 6y = 12 →
  19. 19.3x + 6y = 39 and x − 2y = 1 →
  20. 20.8x + 3y = −45 and 3x + 8y = −10 →
  21. 21.3x + 4y = 36 and 2x + 2y = 20 →
  22. 22.8x + 6y = −38 and 6x + 8y = −18 →
  23. 23.3x − 3y = 51 and 2x − 6y = 66 →
  24. 24.6x + 2y = 32 and 2x + 6y = −16 →
  25. 25.6x + 5y = 48 and 5x − 3y = −3 →
  26. 26.8x + 7y = 43 and 7x + 8y = 47 →
  27. 27.5x + 8y = −60 and 8x + 5y = −57 →
  28. 28.5x + y = −25 and 6x + 3y = −21 →
  29. 29.5x + 5y = −20 and 5x + 4y = −11 →
  30. 30.7x + 6y = 17 and 6x + 7y = 22 →
  31. 31.x − 4y = 20 and 2x − 3y = 20 →
  32. 32.3x + 2y = −30 and 2x + 3y = −35 →
  33. 33.4x + 4y = 16 and 3x − 5y = 36 →
  34. 34.6x − 4y = 36 and 3x + 6y = 42 →
  35. 35.6x + 5y = 29 and 5x + 5y = 25 →
  36. 36.3x + y = 16 and 2x − 4y = 48 →
  37. 37.2x − 5y = −18 and 2x − 6y = −22 →
  38. 38.6x + y = 24 and x + 6y = −31 →
  39. 39.x − y = 4 and 6x + y = 10 →
  40. 40.3x + 5y = −2 and 4x + 4y = 0 →

Answer key

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

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