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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 10 · 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 + 2y = 14 and 2x + 3y = 22 →
  2. 2.x + 7y = −7 and 7x + y = 47 →
  3. 3.2x + 6y = 6 and 6x + 2y = −14 →
  4. 4.4x + 2y = −18 and 2x + 4y = −24 →
  5. 5.5x + 3y = −67 and 3x + 5y = −69 →
  6. 6.5x − 2y = −56 and x + 3y = 16 →
  7. 7.8x + 3y = 37 and 3x + 8y = 62 →
  8. 8.6x + 2y = −22 and 5x + y = −23 →
  9. 9.2x + 2y = 26 and 5x + y = 33 →
  10. 10.8x + 9y = −23 and 9x + 8y = −11 →
  11. 11.x + 6y = −5 and 6x + y = 5 →
  12. 12.x − 6y = −28 and x − 3y = −10 →
  13. 13.6x + 3y = 24 and x + 6y = −18 →
  14. 14.2x + 3y = −16 and 3x + 2y = −14 →
  15. 15.8x + 7y = 103 and 7x + 8y = 107 →
  16. 16.5x − 3y = 22 and 2x + 5y = −16 →
  17. 17.5x + 3y = 19 and 3x + 4y = 18 →
  18. 18.8x + 6y = 48 and 6x + 8y = 50 →
  19. 19.4x + 5y = 45 and 5x + 4y = 45 →
  20. 20.5x + 5y = 55 and 3x + y = 15 →
  21. 21.5x + 2y = −9 and 2x + 5y = −12 →
  22. 22.8x + 5y = 8 and 5x + 8y = −34 →
  23. 23.4x + 4y = −40 and 3x + 4y = −39 →
  24. 24.2x − 4y = 14 and 5x + 5y = −85 →
  25. 25.6x + 6y = 48 and 2x + 5y = 22 →
  26. 26.x + 3y = 13 and 6x + 6y = 6 →
  27. 27.4x + 2y = 18 and 3x − 2y = −11 →
  28. 28.x − 4y = −39 and 5x − 3y = −59 →
  29. 29.6x + 2y = 20 and 6x + 5y = 14 →
  30. 30.x + 3y = 35 and 4x − 2y = 14 →
  31. 31.x + 7y = 8 and 7x + y = 8 →
  32. 32.3x − 5y = 43 and 2x − 2y = 22 →
  33. 33.x + 4y = −18 and 2x − 3y = −3 →
  34. 34.6x + 2y = −26 and 2x − y = −12 →
  35. 35.5x + 2y = 33 and 5x + 6y = 49 →
  36. 36.3x − 2y = 11 and x − 6y = 25 →
  37. 37.x + 3y = 8 and 3x + y = 0 →
  38. 38.5x + 7y = 26 and 7x + 5y = −2 →
  39. 39.3x + 5y = −60 and x + 5y = −50 →
  40. 40.x + 4y = −21 and 2x + 4y = −26 →

Answer key

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

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