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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 467 · 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 + 7y = −38 and 7x + 2y = 2 →
  2. 2.x − 3y = 14 and 5x − y = 42 →
  3. 3.4x + y = 9 and x + 4y = 6 →
  4. 4.5x + 2y = 32 and 3x + 5y = 23 →
  5. 5.5x − y = −32 and 2x + y = −10 →
  6. 6.5x + 5y = 15 and 4x + 2y = 20 →
  7. 7.x + 3y = 1 and 2x − 2y = −6 →
  8. 8.5x + 7y = −33 and 7x + 5y = −27 →
  9. 9.8x + 9y = 65 and 9x + 8y = 54 →
  10. 10.5x + 2y = 29 and x − y = 3 →
  11. 11.6x + 3y = −39 and x − 3y = −24 →
  12. 12.4x + y = −35 and 2x + 2y = −28 →
  13. 13.5x + 3y = −1 and 2x + 4y = 22 →
  14. 14.4x + y = −26 and x − 6y = −44 →
  15. 15.2x + 3y = 0 and 3x + 2y = −5 →
  16. 16.5x − 3y = −8 and 2x + 3y = 1 →
  17. 17.9x + y = 43 and x + 9y = 67 →
  18. 18.5x + y = 12 and x + 5y = 36 →
  19. 19.9x + 6y = 63 and 6x + 9y = 27 →
  20. 20.6x − 3y = −15 and x + y = −4 →
  21. 21.x + 9y = 22 and 9x + y = 38 →
  22. 22.4x + 3y = 13 and 3x + 4y = 8 →
  23. 23.5x + 4y = 41 and 4x + 5y = 49 →
  24. 24.x + y = −2 and 3x + y = 8 →
  25. 25.3x + 8y = 4 and 8x + 3y = 29 →
  26. 26.2x + 5y = 14 and 3x + 5y = 6 →
  27. 27.4x + y = 18 and x + y = 9 →
  28. 28.x + y = −3 and 4x + 6y = −10 →
  29. 29.8x + 6y = 12 and 6x + 8y = 2 →
  30. 30.6x + 3y = 30 and 5x − 5y = 85 →
  31. 31.4x + y = −12 and 5x − 4y = 27 →
  32. 32.2x + 5y = 1 and 5x + 2y = 13 →
  33. 33.3x − 2y = −19 and 4x − 3y = −24 →
  34. 34.x + 6y = −55 and 4x + 2y = −22 →
  35. 35.6x + 5y = 61 and 5x − 5y = 5 →
  36. 36.5x − 2y = −9 and 2x + 2y = 16 →
  37. 37.x + 3y = 18 and 3x + y = 22 →
  38. 38.4x + 3y = −18 and 3x + 4y = −10 →
  39. 39.2x + 6y = 52 and 2x + y = 12 →
  40. 40.3x − 6y = 42 and 4x + 4y = −52 →

Answer key

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

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