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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 46 · 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 + 4y = 51 and 2x + 3y = 36 →
  2. 2.6x − 3y = 15 and 4x + 4y = 40 →
  3. 3.4x − 5y = −3 and x − 3y = −13 →
  4. 4.2x + 4y = −22 and 2x + 3y = −21 →
  5. 5.5x − 4y = 37 and 6x − 4y = 38 →
  6. 6.3x − 4y = 10 and 6x + 4y = 8 →
  7. 7.3x + 2y = −5 and 2x − 3y = 27 →
  8. 8.6x − 2y = 22 and 2x + y = 9 →
  9. 9.6x + 2y = 54 and 2x + 6y = 50 →
  10. 10.6x + 2y = −24 and 4x + 5y = 17 →
  11. 11.2x + 6y = −48 and x + y = −6 →
  12. 12.9x + 5y = −60 and 5x + 9y = −52 →
  13. 13.7x + 3y = −31 and 3x + 7y = 21 →
  14. 14.2x + 5y = 53 and 5x + 2y = 59 →
  15. 15.6x + 4y = −38 and x + 4y = −13 →
  16. 16.5x + 9y = 83 and 9x + 5y = 71 →
  17. 17.9x + 3y = 27 and 3x + 9y = 57 →
  18. 18.x + 5y = 2 and 4x + 2y = −10 →
  19. 19.x − 5y = 24 and 5x + y = 42 →
  20. 20.4x + 4y = −8 and 3x + 4y = 1 →
  21. 21.x + y = 2 and 2x − y = 1 →
  22. 22.5x − 6y = −89 and 6x + 4y = −6 →
  23. 23.6x + 5y = 9 and 4x − y = −33 →
  24. 24.4x + y = −19 and x + 4y = 29 →
  25. 25.2x + 3y = 11 and 3x + 2y = 9 →
  26. 26.2x + 3y = 1 and 3x + 2y = 4 →
  27. 27.4x + 6y = −18 and 4x + 2y = 18 →
  28. 28.x + 4y = 12 and 6x + 2y = 28 →
  29. 29.2x + 3y = 19 and 3x + 2y = 26 →
  30. 30.2x + 4y = 22 and 2x + 2y = 14 →
  31. 31.2x + y = 21 and x + 2y = 18 →
  32. 32.2x + 4y = 34 and 6x + 4y = 62 →
  33. 33.x + y = −7 and 2x + 3y = −20 →
  34. 34.x + 6y = 48 and 3x − 6y = −24 →
  35. 35.9x + y = −89 and x + 9y = −81 →
  36. 36.4x − 6y = 0 and 4x + y = −14 →
  37. 37.2x + 4y = 14 and x − y = 10 →
  38. 38.2x − 2y = 10 and x + 2y = 8 →
  39. 39.5x + 3y = 5 and 3x − 4y = 32 →
  40. 40.3x + 5y = 55 and 5x + 3y = 49 →

Answer key

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

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