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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 96 · 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. 1.2x + y = 14 and x − 3y = −14 →
  2. 2.x + 7y = 69 and 7x + y = 51 →
  3. 3.x + y = −1 and 3x + y = 11 →
  4. 4.5x − 6y = 47 and 2x + 3y = −19 →
  5. 5.7x + y = 53 and x + 7y = 35 →
  6. 6.4x + 2y = −18 and 2x + 4y = 18 →
  7. 7.2x + 6y = 22 and 6x + 3y = 36 →
  8. 8.x + 5y = −16 and 5x + 4y = 4 →
  9. 9.6x + 8y = −16 and 8x + 6y = 16 →
  10. 10.2x + 7y = 43 and 7x + 2y = 38 →
  11. 11.x + 5y = 27 and 2x + y = 9 →
  12. 12.3x − 6y = 3 and 5x + y = −6 →
  13. 13.6x − y = 18 and 5x + 4y = −14 →
  14. 14.4x + 6y = 40 and 6x + 6y = 42 →
  15. 15.2x + 8y = 26 and 8x + 2y = 44 →
  16. 16.5x + 3y = 20 and 4x − 6y = −26 →
  17. 17.6x + 6y = 6 and 3x − 3y = −21 →
  18. 18.4x + y = 14 and 2x + y = 8 →
  19. 19.2x − 2y = −6 and 5x + y = −9 →
  20. 20.2x + 2y = 8 and 4x − y = 11 →
  21. 21.4x + 4y = 4 and 6x − y = 13 →
  22. 22.3x + 5y = 38 and 5x + 3y = 42 →
  23. 23.6x + y = 47 and x + 6y = 37 →
  24. 24.6x − 5y = 24 and 2x + 2y = 30 →
  25. 25.4x − 3y = 9 and 5x + y = 35 →
  26. 26.3x − 6y = −48 and 2x + 6y = 8 →
  27. 27.2x − 4y = 12 and x + 5y = 13 →
  28. 28.6x + 9y = 33 and 9x + 6y = 27 →
  29. 29.6x + 4y = 52 and x + 5y = 39 →
  30. 30.3x + 3y = −9 and 5x + 6y = −22 →
  31. 31.3x + 9y = 3 and 9x + 3y = −63 →
  32. 32.5x − 4y = 4 and 4x + 5y = 36 →
  33. 33.9x + 3y = −27 and 3x + 9y = 63 →
  34. 34.3x + 4y = −12 and 4x + 3y = 5 →
  35. 35.7x + 2y = 43 and 2x + 7y = −7 →
  36. 36.2x + 5y = −17 and 5x + 2y = 10 →
  37. 37.2x + 9y = −35 and 9x + 2y = −42 →
  38. 38.x − 4y = −11 and 3x + 2y = 23 →
  39. 39.4x − y = −1 and 6x − y = 1 →
  40. 40.6x + 5y = 54 and 5x + 5y = 50 →

Answer key

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

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