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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 634 · 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. 1.4x − 6y = −58 and x − 6y = −37 →
  2. 2.4x + 8y = 52 and 8x + 4y = 68 →
  3. 3.4x + 5y = 1 and 5x + 4y = 17 →
  4. 4.5x + 6y = −7 and 6x − 3y = −39 →
  5. 5.x + 2y = 3 and 2x + y = 3 →
  6. 6.x + 9y = −38 and 9x + y = 58 →
  7. 7.x + 4y = 22 and 4x + y = 13 →
  8. 8.5x − 2y = −7 and 3x + y = 9 →
  9. 9.x + 9y = 69 and 9x + y = 61 →
  10. 10.5x + 3y = 48 and 2x + 2y = 20 →
  11. 11.6x + 5y = 72 and 5x + y = 41 →
  12. 12.5x + 6y = −9 and 5x + 2y = −13 →
  13. 13.2x + 6y = 24 and 6x + 2y = −24 →
  14. 14.x + 5y = 29 and 4x − 3y = 24 →
  15. 15.7x + y = −9 and x + 7y = 33 →
  16. 16.x − y = 0 and 2x + 3y = 15 →
  17. 17.7x + 6y = −10 and 6x + 7y = −3 →
  18. 18.4x − 2y = −10 and 6x + y = −19 →
  19. 19.x + 6y = 35 and 5x − 6y = −5 →
  20. 20.2x − 5y = −37 and 2x + 2y = 26 →
  21. 21.4x + 6y = 42 and 6x + 4y = 38 →
  22. 22.x + 4y = 22 and 2x + 5y = 29 →
  23. 23.8x + 2y = 36 and 2x + 8y = 24 →
  24. 24.4x + 3y = −29 and 3x + 4y = −34 →
  25. 25.4x − 4y = −12 and 3x + 4y = 33 →
  26. 26.x + y = 3 and x + 5y = 19 →
  27. 27.x + 3y = −2 and 6x + y = −29 →
  28. 28.2x + 2y = 24 and 2x + y = 21 →
  29. 29.3x + 9y = 24 and 9x + 3y = 24 →
  30. 30.5x − y = 7 and 5x − 3y = 1 →
  31. 31.4x + 7y = 72 and 7x + 4y = 60 →
  32. 32.4x − y = 2 and 2x − 4y = −6 →
  33. 33.6x + 2y = −36 and 5x + 5y = −20 →
  34. 34.x + 6y = −31 and 6x + y = −11 →
  35. 35.6x + 7y = 82 and 7x + 6y = 87 →
  36. 36.4x + 3y = −17 and 3x + 2y = −13 →
  37. 37.6x + 7y = −31 and 7x + 6y = −21 →
  38. 38.2x + 9y = 35 and 9x + 2y = 42 →
  39. 39.2x − y = 8 and 3x − 5y = 33 →
  40. 40.9x + 8y = −32 and 8x + 9y = −19 →

Answer key

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

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