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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 439 · 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 + 3y = 25 and 3x + 2y = 25 →
  2. 2.x + 3y = −11 and 2x − 6y = −10 →
  3. 3.3x + 3y = 3 and 5x + 2y = 17 →
  4. 4.2x − 2y = 4 and 6x − 2y = 24 →
  5. 5.3x + y = −3 and 2x + 2y = −14 →
  6. 6.3x − 5y = 27 and 4x − y = −15 →
  7. 7.3x − 4y = −1 and x − 4y = −19 →
  8. 8.9x + 7y = 33 and 7x + 9y = 47 →
  9. 9.x − 3y = 10 and 6x − 3y = −15 →
  10. 10.3x + 2y = 25 and 4x + y = 25 →
  11. 11.3x + 2y = −20 and x + 5y = 2 →
  12. 12.4x − 5y = −8 and x + y = 16 →
  13. 13.5x + 6y = 13 and 2x + 2y = 4 →
  14. 14.x − 2y = 9 and 3x + 3y = 18 →
  15. 15.4x + 2y = 8 and 2x + 4y = 22 →
  16. 16.6x − 3y = −27 and 5x + 6y = −14 →
  17. 17.4x − 2y = −28 and 6x + 3y = −18 →
  18. 18.6x − 3y = 33 and 5x − 5y = 25 →
  19. 19.4x − 4y = −8 and 6x − 4y = −4 →
  20. 20.5x + 4y = 42 and 3x + 6y = 36 →
  21. 21.x − 3y = −10 and 3x + 4y = 22 →
  22. 22.9x + 6y = 75 and 6x + 9y = 90 →
  23. 23.9x + 7y = 130 and 7x + 9y = 126 →
  24. 24.5x + 3y = 13 and 3x − 4y = −27 →
  25. 25.4x + 4y = 12 and 4x − 6y = 52 →
  26. 26.2x − 3y = 21 and x + y = 3 →
  27. 27.x − y = 2 and 2x + 6y = −36 →
  28. 28.5x − 3y = −69 and x + 3y = 15 →
  29. 29.5x + 5y = 10 and 6x + 2y = −20 →
  30. 30.3x + 5y = 12 and x − 3y = 18 →
  31. 31.4x + 5y = −47 and 5x + 4y = −52 →
  32. 32.6x + y = 13 and 2x − 5y = −33 →
  33. 33.9x + 5y = −46 and 5x + 9y = 18 →
  34. 34.3x + 9y = 48 and 9x + 3y = 48 →
  35. 35.x − 6y = 34 and 3x − 3y = 12 →
  36. 36.7x + 3y = −20 and 3x + 7y = 20 →
  37. 37.x − 2y = −4 and 6x − 2y = 26 →
  38. 38.5x + y = 15 and x + y = 7 →
  39. 39.x + 3y = 26 and 3x − 2y = −21 →
  40. 40.x + 5y = 12 and 4x + 5y = 33 →

Answer key

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

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