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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 347 · 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 = 6 and 3x + y = −6 →
  2. 2.6x + y = 63 and 6x + 5y = 99 →
  3. 3.5x + 2y = 31 and 3x + y = 18 →
  4. 4.2x − 3y = 36 and 6x − 4y = 78 →
  5. 5.2x + y = 13 and 3x + 5y = 51 →
  6. 6.3x + y = 3 and 6x + 5y = −21 →
  7. 7.5x + 2y = −35 and 2x + 5y = −35 →
  8. 8.6x + 3y = 42 and 4x − 6y = 60 →
  9. 9.3x + 3y = 0 and 2x + 6y = 8 →
  10. 10.3x + 4y = 31 and x − 3y = −20 →
  11. 11.4x + 6y = 70 and 2x + 4y = 42 →
  12. 12.4x − y = 21 and x + y = 14 →
  13. 13.2x + y = −11 and 5x + 6y = −17 →
  14. 14.6x + y = 62 and x − 4y = −23 →
  15. 15.4x + 3y = 60 and 3x + 4y = 59 →
  16. 16.2x − y = 2 and x + y = 7 →
  17. 17.4x + y = 15 and 3x − 2y = 3 →
  18. 18.3x + 3y = 0 and 5x − 5y = −80 →
  19. 19.3x + 3y = −12 and x − y = 10 →
  20. 20.6x − 3y = 3 and 2x + 2y = 28 →
  21. 21.2x + 5y = 48 and x + 2y = 21 →
  22. 22.7x + y = 12 and x + 7y = −12 →
  23. 23.5x + 4y = −71 and 4x + 5y = −73 →
  24. 24.3x − y = −17 and x + 4y = 3 →
  25. 25.x + 5y = 12 and x + 6y = 13 →
  26. 26.5x + y = −18 and 6x + y = −22 →
  27. 27.4x − y = −38 and 5x + 6y = −4 →
  28. 28.5x − y = −50 and 3x − y = −32 →
  29. 29.3x + 8y = −71 and 8x + 3y = −61 →
  30. 30.x + y = −7 and 5x + y = −3 →
  31. 31.7x + 8y = 78 and 8x + 7y = 72 →
  32. 32.6x − 6y = −12 and 6x + 6y = 24 →
  33. 33.3x − y = 11 and 4x + 5y = −17 →
  34. 34.7x + 8y = −18 and 8x + 7y = −27 →
  35. 35.3x + 4y = 30 and 6x + 3y = 45 →
  36. 36.3x − 2y = 23 and 6x − 3y = 45 →
  37. 37.3x + 2y = 10 and 6x − 2y = 44 →
  38. 38.x + 2y = 4 and 2x + y = 5 →
  39. 39.2x + 4y = −50 and 4x + 2y = −52 →
  40. 40.2x + 6y = 22 and 4x + 4y = 28 →

Answer key

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

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