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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 302 · 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. 1.4x − 3y = −8 and 4x + y = −40 →
  2. 2.2x + 5y = −27 and 3x + y = 18 →
  3. 3.5x + 3y = −10 and x − 2y = −15 →
  4. 4.6x + y = −40 and x + 6y = 40 →
  5. 5.5x + 2y = 31 and 4x + y = 20 →
  6. 6.5x + 6y = 58 and x + y = 11 →
  7. 7.9x + 3y = −36 and 3x + 9y = 36 →
  8. 8.7x + 3y = 65 and 3x + 7y = 45 →
  9. 9.x − 6y = 19 and x − 5y = 15 →
  10. 10.3x + 6y = 30 and 6x + 3y = 24 →
  11. 11.5x + 5y = 30 and x + 2y = 9 →
  12. 12.2x + 7y = −27 and 7x + 2y = 18 →
  13. 13.3x + 9y = −3 and 9x + 3y = 15 →
  14. 14.3x + y = 7 and 2x + 3y = −14 →
  15. 15.4x + 3y = 10 and 3x + 4y = 4 →
  16. 16.2x + 3y = −2 and 3x + 2y = −8 →
  17. 17.3x − 6y = 30 and 5x + 2y = −22 →
  18. 18.5x + 6y = −6 and 6x − 3y = −48 →
  19. 19.3x + 9y = 39 and 9x + 3y = 21 →
  20. 20.2x + 2y = 8 and 2x + 6y = 4 →
  21. 21.x + 3y = 4 and 5x + 4y = 9 →
  22. 22.2x + 6y = 44 and 6x + 2y = −12 →
  23. 23.9x + 4y = −68 and 4x + 9y = −88 →
  24. 24.5x + 5y = −5 and 3x + y = 3 →
  25. 25.2x + 9y = −3 and 9x + 2y = −52 →
  26. 26.5x − 6y = −49 and 4x + 6y = 58 →
  27. 27.5x + 3y = 19 and 3x + 5y = 21 →
  28. 28.7x + 2y = 44 and 2x + 7y = −26 →
  29. 29.x + 6y = −2 and 2x − 4y = −20 →
  30. 30.x + 2y = 14 and 3x + 2y = 22 →
  31. 31.2x + 6y = 38 and 3x + 6y = 33 →
  32. 32.4x + 2y = 22 and x + 3y = 8 →
  33. 33.x − 3y = −30 and x + 3y = 12 →
  34. 34.3x + 2y = −38 and 5x + y = −47 →
  35. 35.3x + 2y = 7 and 2x + 6y = −28 →
  36. 36.9x + 4y = −40 and 4x + 9y = 40 →
  37. 37.5x + 6y = 84 and 6x + 5y = 81 →
  38. 38.6x + 2y = −34 and 2x + 3y = −9 →
  39. 39.3x − y = −5 and 4x − 3y = 0 →
  40. 40.3x + 4y = 17 and 4x + 3y = 18 →

Answer key

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

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