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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 670 · 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 − 6y = −28 and 6x + y = 30 →
  2. 2.4x + 5y = −19 and 5x + 4y = −8 →
  3. 3.8x + 5y = −11 and 5x + 8y = −41 →
  4. 4.6x + 3y = −15 and 2x + 3y = −19 →
  5. 5.9x + 4y = 10 and 4x + 9y = 55 →
  6. 6.5x + 3y = 3 and 2x + 3y = 12 →
  7. 7.3x + 4y = −18 and 4x + 3y = −10 →
  8. 8.6x + 5y = −7 and 3x + 6y = −21 →
  9. 9.3x + 6y = 36 and 2x − 2y = 12 →
  10. 10.2x − y = −13 and x − 5y = −38 →
  11. 11.5x + 9y = 101 and 9x + 5y = 81 →
  12. 12.3x + y = 17 and x + 3y = 19 →
  13. 13.2x + 5y = −23 and 3x − 6y = 33 →
  14. 14.4x + 5y = −47 and 5x + 4y = −43 →
  15. 15.5x − 2y = 39 and 6x + 2y = 38 →
  16. 16.x + 5y = −7 and 5x + y = 13 →
  17. 17.5x − y = 3 and 3x + 2y = 7 →
  18. 18.8x + y = 15 and x + 8y = −69 →
  19. 19.4x + 2y = −2 and x + 3y = 7 →
  20. 20.2x + y = 11 and 2x + 6y = 46 →
  21. 21.6x + 5y = 32 and x − 3y = 13 →
  22. 22.9x + y = 20 and x + 9y = −60 →
  23. 23.2x + 9y = −12 and 9x + 2y = 23 →
  24. 24.4x + y = 27 and 6x − 4y = 46 →
  25. 25.9x + y = 57 and x + 9y = 33 →
  26. 26.2x + 4y = 6 and 3x + y = 24 →
  27. 27.7x + 5y = 37 and 5x + 7y = 47 →
  28. 28.2x − 5y = −49 and 5x + 3y = 17 →
  29. 29.8x + 9y = 57 and 9x + 8y = 45 →
  30. 30.4x − 3y = 29 and 5x + y = 41 →
  31. 31.2x − 4y = −26 and 2x + 4y = 38 →
  32. 32.6x + 2y = 20 and 2x + 6y = 28 →
  33. 33.5x + 7y = −51 and 7x + 5y = −33 →
  34. 34.x − 3y = 8 and 6x + y = −9 →
  35. 35.6x − 6y = −48 and 6x + 3y = 15 →
  36. 36.x + 6y = 56 and 2x − 3y = −8 →
  37. 37.3x + 5y = −27 and 5x + y = 21 →
  38. 38.4x − 5y = 36 and x + 5y = −16 →
  39. 39.4x + 5y = 34 and 6x − 6y = 24 →
  40. 40.3x + 7y = −22 and 7x + 3y = 2 →

Answer key

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

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