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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 99 · 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 + 3y = −15 and x − y = −9 →
  2. 2.2x + 2y = −24 and 2x + 4y = −38 →
  3. 3.2x + 8y = 34 and 8x + 2y = 76 →
  4. 4.x − 4y = −28 and x − 2y = −10 →
  5. 5.2x + 2y = −28 and 5x − 3y = 2 →
  6. 6.4x − y = −1 and 5x − 3y = −17 →
  7. 7.2x + 2y = 10 and x + 6y = 0 →
  8. 8.2x + 3y = 0 and x + 2y = −3 →
  9. 9.x − 2y = −14 and 2x − 5y = −37 →
  10. 10.4x + 4y = 20 and x − 5y = −49 →
  11. 11.3x − y = −10 and 5x + 2y = −24 →
  12. 12.5x + 3y = 41 and 4x + 5y = 38 →
  13. 13.2x + 2y = 6 and 5x − 2y = −27 →
  14. 14.3x + 5y = 41 and 2x − 2y = −10 →
  15. 15.6x − 2y = −4 and 4x + 2y = 14 →
  16. 16.3x + 8y = 73 and 8x + 3y = 48 →
  17. 17.x − 6y = 15 and 5x − 2y = 47 →
  18. 18.3x − y = 20 and 3x + 2y = 14 →
  19. 19.6x + 3y = −30 and 3x + 6y = 12 →
  20. 20.3x + 8y = −35 and 8x + 3y = 35 →
  21. 21.6x + 4y = 84 and 4x + y = 41 →
  22. 22.4x + 3y = 23 and 2x + 5y = 15 →
  23. 23.6x + 4y = −8 and 6x − 2y = −14 →
  24. 24.4x − 4y = 44 and 2x − 5y = 34 →
  25. 25.2x − 2y = 2 and 3x − 2y = 6 →
  26. 26.3x + 4y = −17 and 4x + 3y = −18 →
  27. 27.8x + y = 25 and x + 8y = 11 →
  28. 28.x + 2y = −1 and 2x + y = −14 →
  29. 29.4x − 5y = −1 and x + 4y = −37 →
  30. 30.4x − 4y = 20 and x + y = −7 →
  31. 31.3x + 2y = 11 and 5x − 6y = 37 →
  32. 32.4x − 3y = 25 and 4x + 5y = 33 →
  33. 33.3x + 4y = −55 and 4x + 3y = −57 →
  34. 34.2x − 2y = 26 and 4x + 2y = −2 →
  35. 35.6x + 2y = −48 and 4x + 3y = −37 →
  36. 36.4x − 6y = 2 and x + 6y = −7 →
  37. 37.5x + 2y = 12 and 2x + 5y = 9 →
  38. 38.x + 2y = 18 and 2x + y = 21 →
  39. 39.3x + 2y = −22 and 2x + 3y = −18 →
  40. 40.3x − 5y = −18 and 6x + y = 63 →

Answer key

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

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