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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 8 · 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. 1.3x + 7y = 55 and 7x + 3y = 35 →
  2. 2.3x + 2y = 34 and 4x + 4y = 56 →
  3. 3.5x − y = 22 and 3x + y = 18 →
  4. 4.x + y = 4 and 4x + 6y = 20 →
  5. 5.3x + 2y = 17 and 2x + 3y = 23 →
  6. 6.4x − 6y = −12 and 5x + 2y = 23 →
  7. 7.x − y = 8 and x + 4y = −17 →
  8. 8.2x − 3y = −16 and x + 4y = 14 →
  9. 9.3x − y = 1 and 4x − 6y = −36 →
  10. 10.x − 2y = −2 and x + 2y = 10 →
  11. 11.x + 4y = 17 and x + 5y = 19 →
  12. 12.9x + 2y = −13 and 2x + 9y = 57 →
  13. 13.6x − 6y = −6 and x − 4y = −22 →
  14. 14.x + 4y = 21 and 4x + y = 39 →
  15. 15.x + 2y = −17 and 5x + y = −4 →
  16. 16.8x + 4y = 68 and 4x + 8y = 88 →
  17. 17.x + 3y = 30 and 6x − 6y = −12 →
  18. 18.3x + 6y = −27 and 6x + 2y = 36 →
  19. 19.2x + 5y = −54 and 5x − 3y = −11 →
  20. 20.2x + 6y = 66 and 2x + 2y = 34 →
  21. 21.6x + 7y = −12 and 7x + 6y = −1 →
  22. 22.2x + y = 18 and 5x + 5y = 50 →
  23. 23.6x + y = 50 and x + 3y = 14 →
  24. 24.2x + 7y = −41 and 7x + 2y = 14 →
  25. 25.4x − 2y = −28 and 4x + 3y = −8 →
  26. 26.9x + 8y = 67 and 8x + 9y = 69 →
  27. 27.5x − 2y = 29 and 5x − y = 22 →
  28. 28.3x + 2y = 37 and 4x + 2y = 44 →
  29. 29.x + 2y = −18 and x + 3y = −23 →
  30. 30.4x + 2y = 34 and 2x + 4y = 20 →
  31. 31.5x − y = 28 and 2x + y = 21 →
  32. 32.3x − y = 19 and x + y = 13 →
  33. 33.6x + 5y = −9 and x − 3y = 10 →
  34. 34.4x − 6y = 52 and 5x + y = 14 →
  35. 35.x − 6y = 31 and 3x − 2y = 13 →
  36. 36.x + 5y = 26 and 6x + 5y = −19 →
  37. 37.2x − 2y = 16 and 5x − 4y = 37 →
  38. 38.3x − 2y = −37 and 5x + y = −40 →
  39. 39.6x + 8y = −18 and 8x + 6y = 18 →
  40. 40.5x + 8y = 21 and 8x + 5y = −21 →

Answer key

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

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