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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 193 · 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 + 2y = −69 and 2x + 9y = −41 →
  2. 2.x − y = 5 and 5x + 5y = −35 →
  3. 3.3x + y = −17 and 2x − 5y = −17 →
  4. 4.2x + 2y = −16 and 4x + 6y = −30 →
  5. 5.2x − 3y = −6 and 6x − 6y = 6 →
  6. 6.x + 3y = 13 and 4x + 3y = 34 →
  7. 7.3x + y = −22 and 4x + 3y = −31 →
  8. 8.5x + y = −32 and x + 2y = 8 →
  9. 9.3x + 6y = 51 and 5x + 3y = 29 →
  10. 10.x + 2y = 10 and 3x + y = 0 →
  11. 11.3x − y = −10 and 4x − 4y = −8 →
  12. 12.x + 3y = 5 and 3x + y = −17 →
  13. 13.4x + 2y = −36 and 6x + y = −42 →
  14. 14.6x + y = 16 and x + 6y = −44 →
  15. 15.8x + 5y = 107 and 5x + 8y = 101 →
  16. 16.2x − 4y = −4 and 5x − 6y = 2 →
  17. 17.5x + y = 1 and 3x + 4y = 21 →
  18. 18.3x + 3y = 15 and 5x + 6y = 28 →
  19. 19.8x + 9y = 92 and 9x + 8y = 95 →
  20. 20.5x + 4y = 61 and 2x − 5y = −35 →
  21. 21.3x + 2y = −8 and 2x + 5y = 13 →
  22. 22.6x + y = 20 and x + 6y = 15 →
  23. 23.4x + 2y = −2 and 6x + y = 11 →
  24. 24.5x − 4y = −7 and 6x − 6y = −6 →
  25. 25.6x + 2y = 22 and 6x − 4y = 64 →
  26. 26.3x + 6y = 45 and x + 4y = 25 →
  27. 27.3x + 3y = 42 and 2x + 5y = 55 →
  28. 28.5x + 3y = 1 and 3x + 5y = 23 →
  29. 29.6x + 6y = 66 and 2x − 2y = −2 →
  30. 30.5x + 5y = −10 and x + 3y = −20 →
  31. 31.2x + 6y = 10 and 3x + 6y = 12 →
  32. 32.3x + 5y = 39 and x − 2y = 2 →
  33. 33.4x + 5y = 1 and 5x + y = 38 →
  34. 34.5x + 5y = −10 and 6x + y = 13 →
  35. 35.x + 3y = 18 and 4x + 3y = 45 →
  36. 36.6x + 9y = 21 and 9x + 6y = −6 →
  37. 37.3x + 4y = 21 and 2x − 5y = −9 →
  38. 38.3x − 2y = 36 and x + 6y = −28 →
  39. 39.5x + 7y = 33 and 7x + 5y = 27 →
  40. 40.3x + 6y = 27 and 3x − 5y = 16 →

Answer key

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

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