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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 775 · 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. 1.4x + 5y = 34 and 5x + 6y = 42 →
  2. 2.x + 2y = 16 and 6x − 3y = −9 →
  3. 3.2x + 5y = 9 and x + 2y = 4 →
  4. 4.x + 5y = 34 and 5x + y = 26 →
  5. 5.5x + 4y = −2 and x + 3y = 4 →
  6. 6.6x + 2y = −50 and 2x + 6y = −38 →
  7. 7.x + 3y = −21 and 4x − 4y = 12 →
  8. 8.5x + 4y = 54 and 2x − 2y = 0 →
  9. 9.6x + 6y = −18 and 5x + 6y = −10 →
  10. 10.4x − 6y = 8 and 4x + 2y = 40 →
  11. 11.4x + 2y = −6 and 2x − 4y = −28 →
  12. 12.4x + 7y = 41 and 7x + 4y = 47 →
  13. 13.4x + y = 6 and 3x + 6y = 15 →
  14. 14.2x − 2y = −10 and x + 3y = 3 →
  15. 15.x + y = −7 and 6x − 6y = −30 →
  16. 16.3x + 5y = −9 and 5x + 3y = 1 →
  17. 17.3x + 5y = −14 and 5x + 3y = −2 →
  18. 18.6x + 8y = 60 and 8x + 6y = 52 →
  19. 19.x + 4y = 24 and 4x + y = 36 →
  20. 20.5x + 5y = 50 and 4x − 5y = −23 →
  21. 21.4x + 5y = 28 and 5x + 4y = 17 →
  22. 22.5x + 2y = −9 and 2x − 6y = −24 →
  23. 23.x + 5y = 3 and 3x + 3y = −15 →
  24. 24.5x + y = 31 and 4x − 2y = 36 →
  25. 25.2x + 2y = 22 and 2x + 6y = 58 →
  26. 26.4x + 6y = −26 and 3x − y = 19 →
  27. 27.x − 4y = 0 and 5x + 6y = 52 →
  28. 28.9x + 5y = −26 and 5x + 9y = −2 →
  29. 29.5x − 2y = 19 and 2x + y = 13 →
  30. 30.2x + 6y = −14 and 4x − 5y = 57 →
  31. 31.4x − y = 16 and 5x + 5y = −30 →
  32. 32.x − y = 9 and 5x + 5y = 5 →
  33. 33.8x + 5y = 54 and 5x + 8y = 63 →
  34. 34.5x − 2y = 35 and 5x − 6y = 55 →
  35. 35.x + 6y = −56 and 6x + 2y = −30 →
  36. 36.6x + 2y = 70 and 5x + 3y = 69 →
  37. 37.2x + 3y = 7 and 2x + 2y = 0 →
  38. 38.x − 3y = −12 and 2x − 3y = −18 →
  39. 39.9x + y = 21 and x + 9y = −51 →
  40. 40.x + y = 8 and 6x + 2y = 44 →

Answer key

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

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