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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 45 · 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. 1.2x + 6y = 38 and 4x + 3y = 40 →
  2. 2.9x + 4y = 3 and 4x + 9y = −42 →
  3. 3.5x − 6y = −8 and x − 4y = −24 →
  4. 4.9x + 8y = 19 and 8x + 9y = 15 →
  5. 5.6x + 3y = 60 and 3x + 6y = 48 →
  6. 6.4x + 2y = −20 and x − 3y = 9 →
  7. 7.2x + 3y = −20 and 3x + 4y = −27 →
  8. 8.2x + y = 17 and 6x + 5y = 65 →
  9. 9.4x + y = 27 and 3x + 5y = −1 →
  10. 10.3x − 2y = −31 and 4x − 3y = −42 →
  11. 11.x + y = −12 and 4x − 2y = 0 →
  12. 12.4x + 6y = 18 and 2x + 5y = 7 →
  13. 13.6x + y = 32 and x + 6y = −18 →
  14. 14.3x + 6y = −15 and 6x + 3y = −3 →
  15. 15.2x + y = 18 and x + 4y = 30 →
  16. 16.x − 4y = 37 and 4x + 4y = −32 →
  17. 17.2x + 7y = 60 and 7x + 2y = 75 →
  18. 18.8x + 9y = −12 and 9x + 8y = −5 →
  19. 19.6x + 2y = 6 and 2x + 6y = 34 →
  20. 20.3x + 2y = −23 and 2x + 3y = −12 →
  21. 21.6x − 2y = 50 and 3x − 3y = 21 →
  22. 22.2x + 4y = −22 and 2x − 4y = 2 →
  23. 23.3x − 6y = 39 and x − 6y = 21 →
  24. 24.x − 6y = −4 and x + 4y = 6 →
  25. 25.3x − 5y = −28 and 2x + 3y = −6 →
  26. 26.2x + y = 10 and 5x + 6y = 11 →
  27. 27.3x − 3y = −9 and 2x + 3y = 24 →
  28. 28.9x + 2y = −20 and 2x + 9y = 64 →
  29. 29.3x + 2y = 33 and 2x + 3y = 27 →
  30. 30.x − 3y = −12 and 2x + 5y = 53 →
  31. 31.x + 5y = 8 and x − 4y = −19 →
  32. 32.6x − 2y = 28 and 3x + 4y = 19 →
  33. 33.3x + 4y = 19 and 2x − 5y = 5 →
  34. 34.5x + 6y = 32 and 6x + 5y = 23 →
  35. 35.4x + 3y = −4 and 6x + 2y = 14 →
  36. 36.5x + 2y = 43 and 2x + 5y = 34 →
  37. 37.x + 4y = 15 and 4x + y = 15 →
  38. 38.5x + 2y = 28 and 2x + y = 11 →
  39. 39.x + 7y = 28 and 7x + y = 52 →
  40. 40.4x − 4y = −8 and 4x − 6y = −18 →

Answer key

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

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