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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 149 · 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 = 9 and x − 5y = −13 →
  2. 2.7x + 8y = 31 and 8x + 7y = 44 →
  3. 3.5x − 6y = −26 and 3x + y = 12 →
  4. 4.4x − y = −26 and 4x − 5y = −50 →
  5. 5.9x + 7y = 10 and 7x + 9y = 22 →
  6. 6.x + 6y = 27 and 6x + y = −13 →
  7. 7.5x + 6y = 11 and 6x + 2y = 8 →
  8. 8.x + 6y = −21 and 2x − 2y = 14 →
  9. 9.2x + 6y = 16 and 5x − 2y = −28 →
  10. 10.4x + 9y = 35 and 9x + 4y = 30 →
  11. 11.x − 6y = −31 and 3x − 3y = −33 →
  12. 12.5x + 4y = 64 and 4x − y = 26 →
  13. 13.3x + 9y = 87 and 9x + 3y = 69 →
  14. 14.6x + 5y = −58 and 3x + 5y = −49 →
  15. 15.6x − 2y = −64 and 6x − 3y = −69 →
  16. 16.4x + 2y = −8 and x + y = −5 →
  17. 17.3x − 6y = 3 and x − 4y = −3 →
  18. 18.2x − 6y = −50 and 3x + 3y = 33 →
  19. 19.3x + 6y = 33 and 6x + 3y = 21 →
  20. 20.3x + 2y = 37 and 2x + 3y = 38 →
  21. 21.3x + 5y = −18 and 2x + 3y = −9 →
  22. 22.7x + 2y = 26 and 2x + 7y = 1 →
  23. 23.2x + 5y = 42 and 2x + 6y = 48 →
  24. 24.3x − 3y = 33 and 4x + 2y = −10 →
  25. 25.6x + 4y = −38 and x + 3y = −4 →
  26. 26.7x + 5y = 19 and 5x + 7y = 17 →
  27. 27.4x + 2y = −4 and 2x + 2y = −10 →
  28. 28.3x + y = 28 and 2x − y = 7 →
  29. 29.4x − 6y = −46 and 3x + y = 15 →
  30. 30.5x + 5y = 10 and 3x + 6y = −15 →
  31. 31.5x + 2y = 18 and 5x + 5y = 0 →
  32. 32.6x + 7y = 55 and 7x + 6y = 49 →
  33. 33.3x + 2y = 10 and 2x + 3y = 5 →
  34. 34.3x + 4y = 25 and x + 2y = 11 →
  35. 35.5x + y = 5 and x + 6y = −28 →
  36. 36.3x + 4y = 5 and 4x + 3y = 2 →
  37. 37.3x + 9y = 60 and 9x + 3y = 60 →
  38. 38.x + 5y = 34 and x + 4y = 26 →
  39. 39.9x + 4y = −2 and 4x + 9y = −37 →
  40. 40.6x + 5y = −3 and x − y = 5 →

Answer key

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

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