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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 507 · 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 − 5y = −13 and 3x − 4y = −17 →
  2. 2.2x + 7y = −52 and 7x + 2y = −2 →
  3. 3.8x + 2y = −4 and 2x + 8y = 44 →
  4. 4.3x − 3y = 27 and 5x + 4y = 0 →
  5. 5.3x + 2y = −9 and 2x + 6y = −20 →
  6. 6.x + 3y = −18 and 3x + y = 18 →
  7. 7.6x + 2y = 60 and 6x − 4y = 42 →
  8. 8.5x + 5y = 75 and 6x − y = 48 →
  9. 9.x + 2y = 21 and 2x + y = 21 →
  10. 10.3x − 6y = −51 and x + 6y = 39 →
  11. 11.4x + 2y = −12 and 2x + 4y = 12 →
  12. 12.5x + y = 3 and 6x − 2y = 10 →
  13. 13.9x + 3y = 96 and 3x + 9y = 96 →
  14. 14.x − 6y = 21 and x + 3y = 3 →
  15. 15.4x + 6y = 18 and x − 3y = 18 →
  16. 16.6x + 3y = 27 and 3x + 5y = −11 →
  17. 17.2x + y = 11 and x + 2y = 13 →
  18. 18.5x − 5y = −50 and 6x + 3y = −42 →
  19. 19.3x + 5y = −28 and x − 6y = 52 →
  20. 20.2x + 7y = −3 and 7x + 2y = 57 →
  21. 21.x + 5y = 8 and x + 6y = 11 →
  22. 22.2x + 2y = 0 and x + 3y = 14 →
  23. 23.x + 4y = 14 and 6x + 4y = 4 →
  24. 24.4x − 4y = 28 and 2x − 4y = 26 →
  25. 25.6x + 3y = 45 and 6x + 5y = 55 →
  26. 26.3x + 6y = 15 and 6x + 5y = 2 →
  27. 27.2x + 9y = 17 and 9x + 2y = 38 →
  28. 28.9x + 5y = −8 and 5x + 9y = −48 →
  29. 29.2x + 3y = 27 and x + 3y = 18 →
  30. 30.6x − 2y = 2 and 6x + 2y = 34 →
  31. 31.9x + 5y = −3 and 5x + 9y = 17 →
  32. 32.6x + 3y = −3 and 3x + 6y = −15 →
  33. 33.3x + y = 13 and 3x + 2y = 14 →
  34. 34.6x + y = −53 and 2x + y = −17 →
  35. 35.8x + y = −44 and x + 8y = 26 →
  36. 36.x + 6y = 55 and 6x + y = 50 →
  37. 37.x − 3y = 2 and 3x + 4y = 32 →
  38. 38.4x − 5y = 0 and x + 2y = 13 →
  39. 39.2x + 7y = 47 and 7x + 2y = 7 →
  40. 40.6x + 3y = 33 and 2x − 5y = 53 →

Answer key

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

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