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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 29 · 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 + 4y = 10 and 4x + 9y = −10 →
  2. 2.9x + 5y = 111 and 5x + 9y = 99 →
  3. 3.6x + 2y = 50 and 5x − 2y = 49 →
  4. 4.x + 4y = 27 and 6x + 5y = −9 →
  5. 5.x + 6y = 62 and 6x + y = 57 →
  6. 6.3x − 3y = 18 and 2x + 6y = 28 →
  7. 7.4x + 3y = 15 and x + 4y = 33 →
  8. 8.4x + 7y = 34 and 7x + 4y = 43 →
  9. 9.5x + 2y = 43 and 2x + 6y = 64 →
  10. 10.x + 8y = 20 and 8x + y = 34 →
  11. 11.2x + 3y = 28 and x − 3y = −22 →
  12. 12.4x − 6y = 2 and x + 6y = 23 →
  13. 13.5x + y = 11 and x + 5y = 7 →
  14. 14.3x + 3y = 51 and 5x − 5y = −5 →
  15. 15.7x + 5y = −39 and 5x + 7y = −45 →
  16. 16.5x + 8y = −21 and 8x + 5y = −18 →
  17. 17.9x + 4y = 42 and 4x + 9y = 62 →
  18. 18.2x + 6y = −6 and 6x + 2y = −34 →
  19. 19.x − y = −12 and 2x + y = −12 →
  20. 20.4x − 3y = 6 and 5x + 2y = 19 →
  21. 21.2x + 4y = 12 and x + 4y = 18 →
  22. 22.7x + 8y = −121 and 8x + 7y = −119 →
  23. 23.5x − 4y = −4 and 4x − 3y = −2 →
  24. 24.5x + 4y = −36 and 3x − 5y = 8 →
  25. 25.6x + y = 42 and x + 6y = −28 →
  26. 26.6x − 5y = 52 and 6x + 2y = −4 →
  27. 27.6x + 5y = 4 and x + 4y = 26 →
  28. 28.2x + 3y = 19 and 5x − 3y = −5 →
  29. 29.6x − 4y = 24 and 3x + 3y = 42 →
  30. 30.4x + 6y = −2 and 6x + 4y = −18 →
  31. 31.5x + 8y = −53 and 8x + 5y = −77 →
  32. 32.6x + 3y = 75 and 5x + 5y = 80 →
  33. 33.4x + 5y = 19 and 2x − y = −15 →
  34. 34.x − 4y = −27 and 6x + 3y = 0 →
  35. 35.5x + 2y = −19 and 2x + 3y = −12 →
  36. 36.3x + y = −10 and x + 3y = 2 →
  37. 37.6x + 2y = −34 and 5x + y = −25 →
  38. 38.3x + 6y = 30 and 6x + 3y = 6 →
  39. 39.2x − 6y = 0 and x + y = 4 →
  40. 40.3x + 5y = 26 and 5x + 3y = 38 →

Answer key

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

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