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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 589 · 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 + 3y = −21 and 5x + 3y = −45 →
  2. 2.9x + 2y = 25 and 2x + 9y = −3 →
  3. 3.x + 3y = 13 and 3x + y = 15 →
  4. 4.5x − 4y = −14 and 2x + 5y = 34 →
  5. 5.x + 5y = −34 and 5x + y = −26 →
  6. 6.3x + 5y = −11 and 5x − y = −9 →
  7. 7.x − 3y = −14 and 4x + 2y = −28 →
  8. 8.2x + y = 13 and x + 2y = 11 →
  9. 9.2x + 6y = 12 and 4x + 6y = −6 →
  10. 10.x + 5y = −41 and 5x + 6y = −34 →
  11. 11.3x + 7y = −36 and 7x + 3y = −4 →
  12. 12.6x + y = 20 and 2x + 2y = 10 →
  13. 13.7x + 6y = −11 and 6x + 7y = −2 →
  14. 14.4x + 4y = 0 and 3x − 6y = −81 →
  15. 15.7x + 9y = 8 and 9x + 7y = 24 →
  16. 16.4x + 5y = 16 and x + y = 5 →
  17. 17.3x + y = −5 and 4x + 2y = −6 →
  18. 18.4x + 7y = 27 and 7x + 4y = −27 →
  19. 19.5x + 6y = 93 and 5x − 5y = 5 →
  20. 20.2x + 6y = −4 and 2x + 2y = 8 →
  21. 21.6x + y = 63 and x + 6y = 63 →
  22. 22.3x + 6y = 42 and 2x − 3y = −28 →
  23. 23.5x + 2y = −20 and 2x − 3y = −27 →
  24. 24.2x + 3y = 7 and 3x + 2y = 8 →
  25. 25.4x − 4y = −64 and 4x − 6y = −82 →
  26. 26.5x − 5y = 30 and x − 5y = 2 →
  27. 27.x + 5y = 17 and x − y = −1 →
  28. 28.6x + 5y = 89 and 3x + y = 34 →
  29. 29.x + 6y = 51 and 2x + 3y = 39 →
  30. 30.8x + 6y = 20 and 6x + 8y = 22 →
  31. 31.x − 6y = −50 and x − y = −10 →
  32. 32.4x + 6y = 22 and 2x + y = 13 →
  33. 33.4x + 8y = 12 and 8x + 4y = −36 →
  34. 34.2x − 4y = −28 and 6x − 4y = −44 →
  35. 35.6x − 5y = 34 and 4x − 5y = 26 →
  36. 36.9x + 2y = −62 and 2x + 9y = 29 →
  37. 37.x − 5y = 24 and x + 3y = 0 →
  38. 38.2x + 7y = 38 and 7x + 2y = 43 →
  39. 39.6x + 2y = 44 and 2x + 6y = 52 →
  40. 40.7x + y = −40 and x + 7y = 8 →

Answer key

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

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