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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 454 · 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. 1.9x + 3y = 87 and 3x + 9y = 69 →
  2. 2.5x + 2y = 37 and 3x + 2y = 27 →
  3. 3.x + 5y = 26 and 3x + 3y = 18 →
  4. 4.3x + 6y = 33 and 6x + 3y = 12 →
  5. 5.5x + 7y = −4 and 7x + 5y = −20 →
  6. 6.x + 5y = −28 and 3x + 4y = −18 →
  7. 7.x + 6y = −45 and 6x + y = −60 →
  8. 8.9x + 4y = 23 and 4x + 9y = 3 →
  9. 9.5x − 5y = 5 and 2x − 5y = −22 →
  10. 10.7x + y = 44 and x + 7y = −28 →
  11. 11.7x + y = −20 and x + 7y = 4 →
  12. 12.5x + 2y = 33 and 2x + 5y = 30 →
  13. 13.3x + 7y = −43 and 7x + 3y = −47 →
  14. 14.3x + 2y = −5 and 3x + y = −4 →
  15. 15.6x + 5y = 23 and x − 2y = 1 →
  16. 16.4x + 9y = 18 and 9x + 4y = 73 →
  17. 17.x − 6y = 39 and 4x + y = 31 →
  18. 18.5x + 6y = 33 and 3x + 3y = 18 →
  19. 19.5x − 4y = −23 and 4x + 3y = 25 →
  20. 20.x + 8y = 20 and 8x + y = −29 →
  21. 21.6x + 2y = −6 and 3x + 4y = −21 →
  22. 22.9x + 4y = 18 and 4x + 9y = 73 →
  23. 23.3x + 5y = −19 and 5x + 3y = −37 →
  24. 24.x − 2y = 0 and 4x + 5y = 39 →
  25. 25.x + 6y = −45 and 2x + 2y = 0 →
  26. 26.x + 6y = −39 and x − 6y = 45 →
  27. 27.2x − 6y = −34 and 5x − y = 27 →
  28. 28.2x + 5y = −21 and 6x + 2y = −24 →
  29. 29.x + 4y = 0 and 4x − 6y = −22 →
  30. 30.5x − y = −6 and 5x + y = −4 →
  31. 31.4x + 4y = 24 and 5x − y = 18 →
  32. 32.4x + 3y = 41 and 3x + 3y = 33 →
  33. 33.x + 3y = 22 and 5x + 4y = 33 →
  34. 34.x − 2y = −21 and 2x + 2y = 0 →
  35. 35.9x + 4y = 15 and 4x + 9y = 50 →
  36. 36.2x + y = −25 and 3x − y = −20 →
  37. 37.x + 6y = −21 and 5x − 3y = −6 →
  38. 38.3x + y = −11 and 6x + 6y = −6 →
  39. 39.4x − 2y = 40 and 4x + 6y = 24 →
  40. 40.5x + 5y = 25 and 6x + 3y = 18 →

Answer key

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

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