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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 21 · 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. 1.9x + 5y = 14 and 5x + 9y = 14 →
  2. 2.x + 4y = 28 and 3x + 2y = −6 →
  3. 3.3x − 2y = −11 and 5x − 3y = −17 →
  4. 4.4x + 4y = 32 and x + 5y = 4 →
  5. 5.8x + 3y = −55 and 3x + 8y = −55 →
  6. 6.3x − 3y = 24 and 6x − 2y = 36 →
  7. 7.2x + 4y = 38 and 6x − 6y = −48 →
  8. 8.6x + 5y = 48 and 2x + 6y = 42 →
  9. 9.3x − 4y = −36 and 6x + 2y = −12 →
  10. 10.2x − y = −2 and x + 3y = 13 →
  11. 11.7x + 2y = −53 and 2x + 7y = 17 →
  12. 12.2x + 6y = −52 and 3x + 4y = −43 →
  13. 13.3x + 5y = 30 and 4x + 3y = 7 →
  14. 14.3x + 9y = 108 and 9x + 3y = 108 →
  15. 15.x + 2y = 17 and 2x + y = 22 →
  16. 16.2x + 9y = 73 and 9x + 2y = 59 →
  17. 17.6x + y = 31 and 5x + y = 27 →
  18. 18.3x − 6y = −54 and 3x + 3y = 18 →
  19. 19.5x + 4y = −53 and 6x + y = −37 →
  20. 20.2x + y = −4 and x + 2y = 1 →
  21. 21.2x + 4y = 18 and 6x + 4y = 14 →
  22. 22.7x + 5y = −44 and 5x + 7y = −28 →
  23. 23.3x + y = 6 and x + 3y = 26 →
  24. 24.5x + 4y = 24 and 4x + 5y = 21 →
  25. 25.7x + 3y = 18 and 3x + 7y = −38 →
  26. 26.6x + 7y = −6 and 7x + 6y = −20 →
  27. 27.2x + y = −11 and 5x + 3y = −31 →
  28. 28.4x + 9y = 59 and 9x + 4y = 19 →
  29. 29.2x + 9y = 25 and 9x + 2y = −3 →
  30. 30.2x + y = −7 and x + 2y = −17 →
  31. 31.3x + 6y = 60 and 6x − y = 29 →
  32. 32.2x − y = 15 and 2x + y = 5 →
  33. 33.3x + 5y = 7 and 4x + 3y = 24 →
  34. 34.6x + 5y = −20 and 5x + 6y = −13 →
  35. 35.x − 4y = −13 and 5x + 2y = 1 →
  36. 36.9x + y = 76 and x + 9y = 44 →
  37. 37.6x + 3y = 36 and 3x + 6y = 27 →
  38. 38.6x + 5y = 42 and 5x + 6y = 46 →
  39. 39.5x + 6y = 24 and 5x + y = 29 →
  40. 40.9x + 6y = −75 and 6x + 9y = −75 →

Answer key

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

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