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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 718 · 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 = 17 and 2x + y = 19 →
  2. 2.2x + 3y = 30 and 2x + 2y = 24 →
  3. 3.6x + 5y = 26 and 5x + 6y = 18 →
  4. 4.2x + 3y = −21 and 3x + 2y = −9 →
  5. 5.3x − 3y = −42 and 3x + 3y = 0 →
  6. 6.2x − 2y = −28 and 6x + 3y = −12 →
  7. 7.x + 7y = 1 and 7x + y = −41 →
  8. 8.2x + 7y = −21 and 7x + 2y = 39 →
  9. 9.3x − 2y = 36 and x − 4y = 42 →
  10. 10.4x + 6y = 24 and 6x + 4y = 26 →
  11. 11.8x + y = −68 and x + 8y = 23 →
  12. 12.5x + 2y = −7 and 4x + 6y = −10 →
  13. 13.x + 6y = 18 and 6x + y = 38 →
  14. 14.2x − y = −20 and x − 4y = −38 →
  15. 15.7x + 3y = −90 and 3x + 7y = −90 →
  16. 16.3x + 4y = 33 and 4x + y = 31 →
  17. 17.2x + 6y = 30 and 5x − 3y = −33 →
  18. 18.6x − 5y = 49 and 4x + 4y = −4 →
  19. 19.3x + 4y = 28 and 4x + 3y = 35 →
  20. 20.x + 9y = −26 and 9x + y = 6 →
  21. 21.x − 6y = 36 and 6x + 2y = −50 →
  22. 22.7x + 9y = 33 and 9x + 7y = 47 →
  23. 23.2x + 7y = 32 and 7x + 2y = −23 →
  24. 24.2x + 2y = 8 and 6x + 5y = 25 →
  25. 25.4x + 5y = 34 and 5x + 5y = 35 →
  26. 26.3x + 9y = −81 and 9x + 3y = −99 →
  27. 27.4x + 7y = 27 and 7x + 4y = 39 →
  28. 28.6x − 2y = −28 and 3x + 2y = 10 →
  29. 29.9x + 2y = −69 and 2x + 9y = 36 →
  30. 30.5x − 4y = −17 and 6x + y = 26 →
  31. 31.2x + y = −11 and 3x − 2y = 15 →
  32. 32.7x + y = −45 and x + 7y = −27 →
  33. 33.5x − 3y = 48 and x + 4y = −18 →
  34. 34.2x + 7y = 58 and 7x + 2y = 23 →
  35. 35.x + 3y = 17 and 4x − y = 29 →
  36. 36.2x + 7y = 10 and 7x + 2y = −10 →
  37. 37.4x + 8y = −44 and 8x + 4y = 8 →
  38. 38.2x + y = 17 and 2x + 4y = 44 →
  39. 39.3x + 5y = −14 and x + 6y = 4 →
  40. 40.3x + 6y = 12 and x − 2y = −16 →

Answer key

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

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