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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 316 · 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. 1.3x + 4y = 17 and 4x + 5y = 21 →
  2. 2.x + 3y = −15 and 3x + y = 3 →
  3. 3.8x + 9y = −47 and 9x + 8y = −55 →
  4. 4.2x + y = 4 and x + 2y = −10 →
  5. 5.8x + 7y = 4 and 7x + 8y = 11 →
  6. 6.x + 3y = −10 and 2x + 5y = −18 →
  7. 7.2x − 6y = 64 and 3x + 6y = −39 →
  8. 8.5x + 7y = 9 and 7x + 5y = 27 →
  9. 9.6x + y = −35 and 4x − 3y = −27 →
  10. 10.x + 2y = 12 and x + 5y = 21 →
  11. 11.3x + 9y = 51 and 9x + 3y = −15 →
  12. 12.9x + 4y = 48 and 4x + 9y = −22 →
  13. 13.5x + 3y = −2 and 3x + 5y = −14 →
  14. 14.2x − y = −12 and 5x − y = −33 →
  15. 15.3x − y = 30 and 3x + 2y = 21 →
  16. 16.3x − 4y = 10 and 5x − 3y = 13 →
  17. 17.4x + 6y = 12 and 2x + 4y = 2 →
  18. 18.x − y = 5 and x − 3y = −1 →
  19. 19.2x − y = 6 and 2x − 4y = 18 →
  20. 20.3x + 2y = −2 and 4x + y = 4 →
  21. 21.2x + 6y = 24 and 6x + 2y = 24 →
  22. 22.3x − 2y = 1 and 2x − 5y = −14 →
  23. 23.2x − y = 15 and 6x + y = 33 →
  24. 24.6x − y = 37 and 5x + 3y = 4 →
  25. 25.6x + 4y = 36 and 6x + 6y = 48 →
  26. 26.x + 6y = 31 and 6x + y = 11 →
  27. 27.2x + 9y = −34 and 9x + 2y = 1 →
  28. 28.2x + 9y = −9 and 9x + 2y = 75 →
  29. 29.7x + 4y = 67 and 4x + 7y = 76 →
  30. 30.x + 6y = −3 and 6x + y = 17 →
  31. 31.2x + y = −8 and 5x + 4y = −14 →
  32. 32.5x + 9y = −23 and 9x + 5y = −19 →
  33. 33.4x + 5y = 64 and 2x − 6y = −36 →
  34. 34.x + 3y = −15 and 3x + 6y = −36 →
  35. 35.4x − 2y = −2 and 5x + y = 29 →
  36. 36.5x + 3y = 31 and 2x − 5y = 0 →
  37. 37.6x + y = 38 and 6x + 6y = 18 →
  38. 38.5x + 2y = 6 and 5x − 5y = −50 →
  39. 39.3x − 2y = −41 and 3x + 3y = −6 →
  40. 40.4x − 5y = −19 and 3x + 3y = 6 →

Answer key

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

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