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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 488 · 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. 1.5x + y = 15 and x + 5y = 27 →
  2. 2.2x + 5y = 37 and 6x + 5y = 41 →
  3. 3.x + 6y = −35 and 6x + y = 35 →
  4. 4.x − 6y = 4 and x − 4y = 0 →
  5. 5.6x + y = −41 and 2x + 3y = −27 →
  6. 6.x + 2y = 12 and 3x + y = −9 →
  7. 7.x + 3y = 11 and x − 4y = −3 →
  8. 8.x + 3y = −2 and 6x − 2y = −52 →
  9. 9.5x − 5y = 0 and 2x + 2y = 16 →
  10. 10.7x + 2y = 3 and 2x + 7y = −12 →
  11. 11.5x − 5y = −10 and 5x + 6y = 67 →
  12. 12.2x + y = 9 and x + 2y = −3 →
  13. 13.3x + 4y = −39 and 4x + 3y = −38 →
  14. 14.7x + 5y = 78 and 5x + 7y = 66 →
  15. 15.x + 5y = −28 and 2x + 5y = −26 →
  16. 16.4x + y = −10 and 3x + y = −8 →
  17. 17.3x + 8y = 33 and 8x + 3y = 33 →
  18. 18.6x + 9y = −48 and 9x + 6y = −57 →
  19. 19.2x + 5y = 43 and 3x − y = 5 →
  20. 20.4x − 5y = −37 and 2x − 2y = −14 →
  21. 21.8x + 6y = 84 and 6x + 8y = 70 →
  22. 22.5x − 5y = 45 and 6x + y = 40 →
  23. 23.9x + 2y = 21 and 2x + 9y = −21 →
  24. 24.4x + 3y = 16 and 4x + 4y = 20 →
  25. 25.7x + 9y = 72 and 9x + 7y = 88 →
  26. 26.5x + 7y = 89 and 7x + 5y = 91 →
  27. 27.4x − 5y = −22 and 3x + 6y = −36 →
  28. 28.2x + 2y = 22 and 4x + 3y = 40 →
  29. 29.3x + 3y = 18 and 2x + 3y = 21 →
  30. 30.x + 3y = 11 and 6x + 5y = 14 →
  31. 31.4x + 4y = 0 and 3x − 2y = −25 →
  32. 32.3x + 6y = 18 and 6x + 3y = −18 →
  33. 33.5x + 3y = 22 and 6x + 5y = 32 →
  34. 34.9x + 6y = 84 and 6x + 9y = 96 →
  35. 35.9x + 7y = −60 and 7x + 9y = −36 →
  36. 36.4x + 3y = 45 and 3x + 3y = 39 →
  37. 37.9x + 5y = −37 and 5x + 9y = −33 →
  38. 38.5x + 4y = −28 and 4x + 5y = −17 →
  39. 39.x − 6y = −56 and 3x + 4y = 8 →
  40. 40.3x − y = 18 and 6x + 6y = 108 →

Answer key

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

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