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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 498 · 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 + 3y = −6 and 5x + 2y = −7 →
  2. 2.5x + 6y = 62 and 6x + 5y = 59 →
  3. 3.x + y = −3 and 2x + 5y = −30 →
  4. 4.5x + 8y = 24 and 8x + 5y = −24 →
  5. 5.x + 4y = −33 and 4x + 4y = −36 →
  6. 6.9x + 7y = 117 and 7x + 9y = 123 →
  7. 7.4x − 6y = 42 and 6x − 4y = 48 →
  8. 8.6x + 6y = −12 and 3x + 2y = 2 →
  9. 9.x + 3y = −12 and 3x + y = −28 →
  10. 10.x + 2y = 5 and 3x + 5y = 17 →
  11. 11.6x − 5y = −53 and 3x + 2y = −22 →
  12. 12.3x − y = 2 and x + 3y = 4 →
  13. 13.5x − 4y = 13 and 2x − 4y = −14 →
  14. 14.x − 2y = 4 and 5x − 3y = 13 →
  15. 15.3x + y = −1 and 3x + 3y = −9 →
  16. 16.2x + 5y = −6 and 3x + 6y = −12 →
  17. 17.x + 7y = 11 and 7x + y = −19 →
  18. 18.3x − 3y = 33 and x − 5y = 31 →
  19. 19.3x + 6y = 39 and x − 2y = −11 →
  20. 20.3x + 2y = 7 and 3x − 3y = 12 →
  21. 21.5x + 2y = −4 and x + y = 1 →
  22. 22.4x + y = −16 and 5x + y = −18 →
  23. 23.x + 2y = 22 and 2x + 5y = 53 →
  24. 24.6x + 6y = 102 and 2x + 4y = 52 →
  25. 25.3x + 5y = 33 and 3x − 6y = −33 →
  26. 26.x − 6y = 3 and 5x + 2y = −49 →
  27. 27.6x − y = 11 and 4x − 3y = −9 →
  28. 28.3x + 9y = 78 and 9x + 3y = 66 →
  29. 29.5x − 6y = −49 and x − y = −9 →
  30. 30.5x + 3y = −21 and 2x + 5y = 22 →
  31. 31.6x + 5y = −43 and 5x + 2y = −38 →
  32. 32.6x + 5y = −8 and 5x + 6y = −14 →
  33. 33.7x + 8y = 135 and 8x + 7y = 135 →
  34. 34.3x + 8y = 23 and 8x + 3y = 43 →
  35. 35.9x + 7y = 31 and 7x + 9y = 17 →
  36. 36.5x − 5y = 5 and 5x − y = 29 →
  37. 37.7x + 6y = 97 and 6x + 7y = 98 →
  38. 38.2x − y = −12 and 2x − 2y = −14 →
  39. 39.x + 2y = −24 and 2x + y = −21 →
  40. 40.3x + 6y = −24 and 4x + 3y = −17 →

Answer key

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

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