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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 776 · 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 − 2y = −43 and 2x + 5y = 22 →
  2. 2.x + 7y = −47 and 7x + y = 7 →
  3. 3.5x + 3y = 51 and x − 5y = −1 →
  4. 4.3x − 2y = −16 and 3x + 3y = −6 →
  5. 5.x + 3y = 21 and 5x + 3y = 45 →
  6. 6.x + 6y = 42 and 2x + y = 18 →
  7. 7.5x + 4y = 21 and 2x + 5y = 5 →
  8. 8.2x − y = −24 and 4x + y = −30 →
  9. 9.6x + 3y = 54 and 3x + 6y = 54 →
  10. 10.x + 4y = −3 and x + 6y = −9 →
  11. 11.6x + 4y = 40 and 2x + 5y = 28 →
  12. 12.2x − 5y = −28 and 6x + 6y = 0 →
  13. 13.x + 6y = 52 and 6x + y = 32 →
  14. 14.4x + 5y = 66 and 5x − 4y = 21 →
  15. 15.6x − 5y = −10 and 2x + 2y = 26 →
  16. 16.6x − 2y = −24 and x + y = 8 →
  17. 17.5x + y = −17 and 5x − 3y = −49 →
  18. 18.4x + 6y = 8 and 6x + 4y = −18 →
  19. 19.x − 3y = −3 and x + 5y = 13 →
  20. 20.x + 9y = 30 and 9x + y = 30 →
  21. 21.4x − 4y = 0 and 3x + y = 24 →
  22. 22.5x − y = 10 and 4x + 4y = −16 →
  23. 23.x + 3y = 22 and 5x + 3y = 26 →
  24. 24.3x + y = 22 and x + 3y = 10 →
  25. 25.x − 4y = 10 and 2x + 2y = 0 →
  26. 26.3x − y = 22 and x − 3y = 18 →
  27. 27.x + 8y = −6 and 8x + y = 15 →
  28. 28.x + 3y = −27 and 4x + 4y = −52 →
  29. 29.7x + 5y = 4 and 5x + 7y = 20 →
  30. 30.2x − y = 10 and 6x + 3y = 42 →
  31. 31.x + 2y = 21 and 6x − 2y = 28 →
  32. 32.4x − 4y = −4 and 4x + 2y = 20 →
  33. 33.x + 8y = −38 and 8x + y = 11 →
  34. 34.3x + 3y = −24 and 4x + 5y = −41 →
  35. 35.x + 9y = 70 and 9x + y = 70 →
  36. 36.6x + 4y = 22 and 2x − 2y = 4 →
  37. 37.5x + 4y = −21 and 4x + 5y = −24 →
  38. 38.3x − 6y = −33 and 2x + 2y = 20 →
  39. 39.5x + 4y = 44 and x − y = 7 →
  40. 40.6x − 4y = 10 and 5x − 6y = 11 →

Answer key

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

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