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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 23 · 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. 1.6x + y = 14 and 2x + y = 10 →
  2. 2.2x + 3y = 4 and 6x − 4y = 38 →
  3. 3.x + 3y = −6 and 3x + y = −26 →
  4. 4.3x + 3y = −30 and 5x + 3y = −38 →
  5. 5.2x − y = −2 and x + 5y = 21 →
  6. 6.2x − 5y = 0 and 6x − 4y = 22 →
  7. 7.2x + 6y = 20 and 2x + 4y = 16 →
  8. 8.5x + 6y = 12 and x + 2y = 0 →
  9. 9.3x + 2y = 2 and x + y = 0 →
  10. 10.2x + 6y = 22 and 6x + 2y = 18 →
  11. 11.2x + 2y = 6 and 5x + 2y = −6 →
  12. 12.x + 9y = −27 and 9x + y = −83 →
  13. 13.5x + 6y = 1 and 5x − 6y = −71 →
  14. 14.5x − y = 44 and 4x + 5y = 41 →
  15. 15.2x + 4y = 22 and 6x + y = 33 →
  16. 16.x + 6y = 31 and x − y = −4 →
  17. 17.x − 6y = −40 and 4x − 2y = −6 →
  18. 18.5x + y = 24 and 6x + 5y = 63 →
  19. 19.2x + y = −9 and x + 2y = 9 →
  20. 20.2x + 6y = 30 and 6x + 2y = −6 →
  21. 21.3x + 2y = 37 and 6x + 6y = 90 →
  22. 22.5x + 5y = 10 and 3x − 4y = −1 →
  23. 23.6x + 6y = 42 and x − 3y = −17 →
  24. 24.3x − y = 7 and 5x + 3y = −7 →
  25. 25.2x − 3y = −5 and 4x + 6y = 2 →
  26. 26.2x + 6y = 0 and 6x + 2y = −48 →
  27. 27.4x − 6y = −46 and 5x + 2y = 28 →
  28. 28.2x + y = 26 and x + 2y = 25 →
  29. 29.x + 5y = 19 and 5x − 2y = 41 →
  30. 30.x − 6y = −21 and 2x + 6y = −6 →
  31. 31.2x + 4y = −28 and 4x + 2y = −20 →
  32. 32.3x + y = −9 and 3x − 3y = 3 →
  33. 33.4x + 3y = −5 and 5x − 2y = −58 →
  34. 34.3x + 5y = 28 and 5x + 5y = 30 →
  35. 35.5x + 2y = 37 and 2x + 5y = 40 →
  36. 36.4x + 4y = 40 and 4x + y = 31 →
  37. 37.x + y = 9 and 2x − 3y = −7 →
  38. 38.4x + 3y = −16 and 3x + 4y = −5 →
  39. 39.4x + 9y = −64 and 9x + 4y = −14 →
  40. 40.5x + 5y = 0 and x + 2y = 2 →

Answer key

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

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