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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 167 · 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. 1.3x − 6y = −21 and 6x + 3y = 3 →
  2. 2.4x + 4y = 40 and x − y = −2 →
  3. 3.5x − 5y = 85 and 3x + 6y = −21 →
  4. 4.3x − 3y = −30 and 6x − 3y = −42 →
  5. 5.8x + 9y = 25 and 9x + 8y = 26 →
  6. 6.6x − y = −37 and 2x + 4y = 18 →
  7. 7.8x + 9y = −12 and 9x + 8y = −22 →
  8. 8.2x + 6y = 46 and 2x + 5y = 38 →
  9. 9.6x + 8y = 90 and 8x + 6y = 78 →
  10. 10.3x − 6y = −9 and 4x + 2y = 28 →
  11. 11.2x + y = 21 and x + 2y = 24 →
  12. 12.6x + y = −48 and x + 6y = 27 →
  13. 13.6x + 9y = −15 and 9x + 6y = 0 →
  14. 14.5x − 6y = −40 and 4x + 3y = 7 →
  15. 15.5x + y = −26 and 6x − 4y = 0 →
  16. 16.2x + 9y = 15 and 9x + 2y = 29 →
  17. 17.5x + 6y = 66 and x + 3y = 24 →
  18. 18.x − 4y = −27 and 4x + 3y = −13 →
  19. 19.7x + 4y = 59 and 4x + 7y = 62 →
  20. 20.x − 3y = −2 and 2x − 4y = −2 →
  21. 21.5x + 4y = −3 and 6x + 3y = −18 →
  22. 22.x + 2y = −19 and 2x − 4y = 10 →
  23. 23.6x − 2y = 14 and x + 2y = 0 →
  24. 24.x + 2y = 17 and x − 2y = −3 →
  25. 25.2x + 5y = 12 and 6x − 6y = −90 →
  26. 26.2x + 2y = 36 and 5x − 2y = 27 →
  27. 27.x + 3y = 19 and 2x + 5y = 30 →
  28. 28.4x − 3y = −31 and x + y = 1 →
  29. 29.2x + 6y = 28 and 4x + 6y = 32 →
  30. 30.2x + y = 12 and x − 6y = −20 →
  31. 31.x + 7y = −8 and 7x + y = 40 →
  32. 32.4x + 5y = −13 and 4x + 6y = −10 →
  33. 33.3x − 4y = 20 and 4x + 6y = 38 →
  34. 34.5x + 3y = 19 and 5x + 2y = 16 →
  35. 35.5x + 3y = 51 and 6x + 2y = 58 →
  36. 36.5x + 2y = −28 and 2x + y = −10 →
  37. 37.x + 3y = 8 and 3x + 2y = −11 →
  38. 38.x + 9y = 34 and 9x + y = 66 →
  39. 39.4x + 7y = −26 and 7x + 4y = 4 →
  40. 40.2x + 7y = −31 and 7x + 2y = −41 →

Answer key

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

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