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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 441 · 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 + 7y = 37 and 7x + y = 19 →
  2. 2.x + 4y = 23 and 2x − 6y = −10 →
  3. 3.x − 5y = 27 and 3x + 2y = −21 →
  4. 4.x − 2y = 0 and x − 4y = 6 →
  5. 5.2x + 9y = 44 and 9x + 2y = −33 →
  6. 6.4x + 3y = 46 and x + 5y = 37 →
  7. 7.3x + 2y = 14 and 6x + y = 43 →
  8. 8.5x + 2y = 3 and 3x − 4y = −19 →
  9. 9.4x + 5y = 26 and x − 2y = −13 →
  10. 10.3x + 6y = 48 and 6x + 3y = 33 →
  11. 11.5x + 6y = −47 and 6x + 5y = −41 →
  12. 12.4x − 4y = 44 and 3x + y = 17 →
  13. 13.4x + 7y = 23 and 7x + 4y = 32 →
  14. 14.2x + 2y = 12 and 3x − 5y = −22 →
  15. 15.x + 8y = 31 and 8x + y = −4 →
  16. 16.6x + y = −41 and 3x + y = −17 →
  17. 17.4x − 2y = −48 and 5x − 6y = −81 →
  18. 18.2x − 2y = 2 and 2x + 5y = 30 →
  19. 19.2x + 3y = 22 and 3x + 2y = 18 →
  20. 20.4x + y = −31 and x − 5y = −34 →
  21. 21.2x − 4y = 32 and 2x + 6y = −8 →
  22. 22.9x + 5y = 78 and 5x + 9y = 62 →
  23. 23.3x + 9y = 27 and 9x + 3y = 57 →
  24. 24.2x + 2y = 4 and 3x + 5y = −6 →
  25. 25.8x + 7y = 96 and 7x + 8y = 99 →
  26. 26.5x + 9y = −4 and 9x + 5y = 4 →
  27. 27.x + 2y = 4 and 2x + y = 14 →
  28. 28.3x − 6y = −51 and 5x + 3y = 32 →
  29. 29.2x + 4y = −38 and 6x − 3y = −24 →
  30. 30.3x + y = 7 and 4x − 5y = −16 →
  31. 31.3x − 2y = −11 and 4x − 4y = −20 →
  32. 32.7x + 5y = −9 and 5x + 7y = −3 →
  33. 33.5x + 2y = 26 and 2x + 4y = 20 →
  34. 34.6x + 2y = 38 and 3x + 5y = 35 →
  35. 35.x + 7y = 61 and 7x + y = −5 →
  36. 36.3x − 5y = 17 and 2x + y = 20 →
  37. 37.8x + 5y = −27 and 5x + 8y = −12 →
  38. 38.5x + 2y = 37 and 5x + 4y = 49 →
  39. 39.4x − 2y = −2 and x − 4y = 24 →
  40. 40.7x + 3y = −8 and 3x + 7y = 48 →

Answer key

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

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