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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 772 · 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. 1.6x − y = −20 and x + 5y = 7 →
  2. 2.2x + y = −17 and 6x − 3y = −33 →
  3. 3.x + 5y = 44 and 4x + 4y = 32 →
  4. 4.2x + y = −3 and x − y = 9 →
  5. 5.5x + 3y = 23 and 6x + 5y = 36 →
  6. 6.x + 3y = 16 and 6x + 3y = 36 →
  7. 7.5x + 3y = 32 and 4x + 4y = 24 →
  8. 8.6x − 2y = 16 and 3x + 5y = −4 →
  9. 9.x − 2y = 6 and 4x + 3y = −53 →
  10. 10.2x + 2y = −16 and 3x − 6y = −33 →
  11. 11.2x + 6y = −28 and 2x + 5y = −23 →
  12. 12.2x + 5y = 4 and x + 2y = 0 →
  13. 13.4x + y = 20 and x + 4y = 20 →
  14. 14.3x + 6y = −18 and 6x + 3y = −27 →
  15. 15.x + 2y = −15 and 2x + y = −21 →
  16. 16.x − 3y = −10 and 3x + 3y = 30 →
  17. 17.3x − 6y = −18 and 3x + y = 24 →
  18. 18.4x − 4y = 4 and x + 6y = −20 →
  19. 19.3x − 4y = 35 and 5x + y = 20 →
  20. 20.5x + 5y = −80 and x − 2y = 5 →
  21. 21.x + 2y = 20 and 5x − 5y = −20 →
  22. 22.x − 6y = −47 and 4x + 6y = 52 →
  23. 23.4x − 3y = 3 and x + 4y = 34 →
  24. 24.2x − y = 7 and 2x + 5y = 61 →
  25. 25.5x − 3y = 17 and 3x + 6y = −21 →
  26. 26.6x + 6y = 66 and 2x − 5y = 1 →
  27. 27.x + 6y = 50 and 5x + 6y = 58 →
  28. 28.9x + 8y = 46 and 8x + 9y = 56 →
  29. 29.7x + 2y = 2 and 2x + 7y = −38 →
  30. 30.3x − 4y = −5 and 5x + 6y = 93 →
  31. 31.x + 4y = 1 and x − y = −4 →
  32. 32.3x + 5y = −12 and 5x + 4y = 6 →
  33. 33.x + 7y = 21 and 7x + y = 51 →
  34. 34.5x + 4y = 37 and 6x − 2y = −10 →
  35. 35.7x + 8y = 16 and 8x + 7y = 29 →
  36. 36.6x − 6y = 66 and 4x + 4y = −12 →
  37. 37.5x + 5y = 25 and 2x + y = 7 →
  38. 38.6x − 4y = 4 and 5x − y = 15 →
  39. 39.x + 2y = −3 and 2x + y = 6 →
  40. 40.x − 6y = −45 and 4x − 2y = −4 →

Answer key

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

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