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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 37 · 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 = 15 and 2x + y = 9 →
  2. 2.2x + y = −18 and 2x + 6y = −28 →
  3. 3.2x + 6y = 50 and x + y = 9 →
  4. 4.x + 8y = 69 and 8x + y = 48 →
  5. 5.6x + y = −47 and 4x − 2y = −50 →
  6. 6.6x + y = −32 and 6x + 3y = −24 →
  7. 7.2x + 4y = 4 and 6x − 2y = −58 →
  8. 8.6x + 4y = 26 and x − 6y = −49 →
  9. 9.3x + y = −21 and x − 5y = −39 →
  10. 10.3x + 9y = 9 and 9x + 3y = −21 →
  11. 11.4x + 5y = 24 and x + y = 5 →
  12. 12.3x − 4y = 18 and 5x + 2y = 4 →
  13. 13.2x + 5y = −38 and 3x − 4y = 35 →
  14. 14.5x + 5y = 45 and 4x + 5y = 39 →
  15. 15.6x + 3y = −39 and 4x + 6y = −22 →
  16. 16.4x + 8y = −60 and 8x + 4y = −72 →
  17. 17.4x − y = −1 and 3x − 5y = −22 →
  18. 18.2x − 2y = 4 and x + 2y = 11 →
  19. 19.8x + 7y = −1 and 7x + 8y = 16 →
  20. 20.x − 4y = 15 and x − 6y = 21 →
  21. 21.x + 4y = 25 and x + 2y = 17 →
  22. 22.6x + 7y = −17 and 7x + 6y = −22 →
  23. 23.5x + 8y = −9 and 8x + 5y = 9 →
  24. 24.4x + 2y = −4 and 3x − 4y = −14 →
  25. 25.5x − 5y = −40 and x + 2y = 7 →
  26. 26.6x + 3y = 6 and 5x + y = 11 →
  27. 27.4x − 6y = −6 and 5x − 4y = 3 →
  28. 28.3x + 3y = −3 and 4x − 5y = 23 →
  29. 29.4x + 3y = −1 and 3x + 4y = −6 →
  30. 30.5x + 3y = 52 and 3x + 5y = 44 →
  31. 31.3x − 3y = −18 and x + y = 8 →
  32. 32.6x + y = 23 and x + 6y = −2 →
  33. 33.2x + 6y = −18 and x + 6y = −21 →
  34. 34.6x + 5y = 31 and 5x + 6y = 35 →
  35. 35.8x + 2y = 76 and 2x + 8y = 64 →
  36. 36.5x + 5y = 20 and 5x − 3y = 4 →
  37. 37.2x + 4y = 14 and 4x + 2y = 10 →
  38. 38.2x − 3y = −29 and 4x + y = −9 →
  39. 39.x − 2y = −1 and 4x − 4y = 4 →
  40. 40.4x + 3y = 25 and 5x − 3y = 11 →

Answer key

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

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