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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 197 · 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 + 6y = 4 and 6x − 2y = −14 →
  2. 2.3x − y = 10 and 4x + y = 32 →
  3. 3.6x − y = −14 and 2x − 2y = −8 →
  4. 4.9x + 4y = −28 and 4x + 9y = 2 →
  5. 5.3x + 5y = 16 and 2x − y = −24 →
  6. 6.6x − 6y = 60 and 6x + 5y = −17 →
  7. 7.2x + 6y = 20 and 6x + 2y = 12 →
  8. 8.x − 2y = −4 and 2x + 2y = 10 →
  9. 9.4x + 7y = −55 and 7x + 4y = −22 →
  10. 10.8x + 2y = 24 and 2x + 8y = −54 →
  11. 11.3x + 5y = −1 and 3x + y = −17 →
  12. 12.2x + 6y = −4 and 6x + 2y = −28 →
  13. 13.x + y = 2 and 5x − 4y = 73 →
  14. 14.2x − 4y = 2 and 2x − 2y = 8 →
  15. 15.4x − 4y = 0 and 2x + y = 21 →
  16. 16.5x + 5y = −20 and 3x + 6y = −27 →
  17. 17.x + 2y = 22 and 6x + 2y = 42 →
  18. 18.x + 5y = −7 and 5x + y = 37 →
  19. 19.4x − 2y = 8 and 4x + 3y = 48 →
  20. 20.5x + 6y = 28 and 3x + 5y = 21 →
  21. 21.7x + 4y = −11 and 4x + 7y = 22 →
  22. 22.3x + 2y = 0 and x + 5y = 39 →
  23. 23.3x + y = 3 and x + 3y = −23 →
  24. 24.3x − 6y = 3 and x + 5y = −34 →
  25. 25.6x + 6y = 96 and 3x + 5y = 62 →
  26. 26.5x + 4y = −27 and 4x + 5y = −36 →
  27. 27.x + 4y = −31 and 4x + y = −4 →
  28. 28.2x + 2y = 8 and 3x + 5y = 2 →
  29. 29.4x − 6y = −50 and 3x + 5y = 10 →
  30. 30.6x − 2y = 56 and 2x − y = 19 →
  31. 31.2x − 4y = 6 and 2x + y = 16 →
  32. 32.2x − 2y = 22 and x + y = 3 →
  33. 33.5x + y = 17 and 3x + 3y = 15 →
  34. 34.2x + 3y = 21 and 3x + 2y = 24 →
  35. 35.5x + 2y = −18 and 2x + 5y = −3 →
  36. 36.2x + 4y = −18 and 6x − 3y = 81 →
  37. 37.4x + 9y = 59 and 9x + 4y = 84 →
  38. 38.4x + 5y = 2 and x − 6y = −14 →
  39. 39.7x + y = −47 and x + 7y = 55 →
  40. 40.x + 4y = 27 and 6x − 4y = −90 →

Answer key

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

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