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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 771 · 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 + 6y = −17 and 6x + y = 3 →
  2. 2.6x − 5y = −33 and 6x + 5y = 57 →
  3. 3.2x + y = 1 and x + 2y = 8 →
  4. 4.3x + y = 4 and x + 3y = −20 →
  5. 5.5x + 3y = 7 and 4x − 2y = 32 →
  6. 6.5x + y = −12 and 6x + y = −13 →
  7. 7.4x + y = 38 and 5x + 3y = 58 →
  8. 8.x + 5y = 9 and 3x + 6y = 9 →
  9. 9.x + y = 2 and 3x + 6y = 30 →
  10. 10.3x + 4y = 21 and 4x + 3y = 14 →
  11. 11.7x + 2y = 62 and 2x + 7y = 37 →
  12. 12.6x − 5y = −65 and x + 5y = 30 →
  13. 13.x + 2y = 6 and 5x − 3y = 43 →
  14. 14.5x − y = 8 and x + 4y = 10 →
  15. 15.4x − 3y = 14 and 5x − 4y = 16 →
  16. 16.3x + 2y = 40 and 4x + 3y = 56 →
  17. 17.x + 5y = 34 and x + 4y = 28 →
  18. 18.x + 2y = −13 and 5x − 3y = 13 →
  19. 19.2x + 6y = 62 and x − 4y = −32 →
  20. 20.7x + 9y = 102 and 9x + 7y = 90 →
  21. 21.3x + 6y = 54 and 6x + 3y = 45 →
  22. 22.5x + 4y = −47 and x + 6y = −51 →
  23. 23.3x + 2y = 33 and x + 6y = 43 →
  24. 24.5x + 3y = 22 and 3x + 5y = 42 →
  25. 25.6x + 6y = 54 and 3x + y = 17 →
  26. 26.4x + 6y = 2 and 2x − y = 21 →
  27. 27.4x + y = 22 and x + 3y = 0 →
  28. 28.3x + y = −12 and x + 3y = 12 →
  29. 29.4x + 2y = 18 and 2x + 4y = 12 →
  30. 30.4x + 5y = −38 and 5x + 4y = −43 →
  31. 31.4x + 9y = −54 and 9x + 4y = −89 →
  32. 32.x + y = 1 and 3x − 4y = −32 →
  33. 33.6x − 2y = −8 and 4x + 5y = 39 →
  34. 34.5x + 5y = 5 and 6x + y = −9 →
  35. 35.4x + 5y = −12 and 6x + 5y = 2 →
  36. 36.4x − y = 27 and 2x + 5y = 63 →
  37. 37.2x + 7y = −13 and 7x + 2y = 22 →
  38. 38.2x + y = −2 and 2x + 3y = −14 →
  39. 39.2x + 6y = 36 and 4x − y = 33 →
  40. 40.4x + 3y = 31 and 3x + 4y = 25 →

Answer key

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

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