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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 879 · 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 + 5y = −12 and x + 3y = −10 →
  2. 2.8x + 7y = 99 and 7x + 8y = 96 →
  3. 3.9x + 3y = −3 and 3x + 9y = 39 →
  4. 4.4x + 9y = −36 and 9x + 4y = 49 →
  5. 5.3x − 3y = −36 and 5x − 4y = −53 →
  6. 6.7x + y = −26 and x + 7y = −38 →
  7. 7.4x + 7y = 34 and 7x + 4y = 43 →
  8. 8.8x + 9y = −41 and 9x + 8y = −27 →
  9. 9.7x + 2y = 1 and 2x + 7y = 26 →
  10. 10.6x + y = −27 and x + 6y = 13 →
  11. 11.x + 5y = 8 and 4x + 3y = 15 →
  12. 12.3x + 6y = 54 and x + 3y = 25 →
  13. 13.7x + 2y = 66 and 2x + 7y = 51 →
  14. 14.6x − 2y = −50 and 2x + y = −10 →
  15. 15.3x − 4y = −23 and 5x − 5y = −30 →
  16. 16.2x + 9y = 19 and 9x + 2y = 47 →
  17. 17.5x + 3y = 41 and x + y = 9 →
  18. 18.6x + 5y = 45 and 5x + 6y = 43 →
  19. 19.9x + 7y = −29 and 7x + 9y = −51 →
  20. 20.x + y = −6 and 2x − 5y = −19 →
  21. 21.2x + y = 13 and x + 2y = 20 →
  22. 22.3x + 4y = 30 and 4x + 3y = 19 →
  23. 23.6x + y = 35 and 5x − y = 20 →
  24. 24.5x + 7y = 5 and 7x + 5y = −17 →
  25. 25.7x + 8y = 15 and 8x + 7y = 15 →
  26. 26.4x + y = 40 and 2x + 4y = 34 →
  27. 27.2x + 5y = 1 and x + 2y = −1 →
  28. 28.6x + 2y = 2 and 2x + 6y = 22 →
  29. 29.8x + 4y = −4 and 4x + 8y = −56 →
  30. 30.x + 4y = −17 and 5x + 6y = −57 →
  31. 31.2x − 2y = −22 and 6x − 2y = −34 →
  32. 32.6x − y = −50 and 5x + 3y = −34 →
  33. 33.x − 4y = −45 and 2x + 2y = 0 →
  34. 34.x + 4y = 5 and 4x + y = 35 →
  35. 35.2x + 3y = 20 and 3x − 2y = 17 →
  36. 36.6x + 5y = 37 and 2x + 2y = 12 →
  37. 37.2x − 6y = 14 and 6x − 5y = 3 →
  38. 38.5x + 6y = 53 and 2x + 4y = 34 →
  39. 39.6x − 3y = 3 and 2x + 5y = 19 →
  40. 40.3x − 3y = 18 and 3x + 3y = −30 →

Answer key

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

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