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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 12 · 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 + 8y = 20 and 8x + 2y = 20 →
  2. 2.x + 5y = 11 and x − y = −13 →
  3. 3.3x − 3y = −3 and 3x − 2y = 4 →
  4. 4.2x + 9y = 87 and 9x + 2y = 45 →
  5. 5.3x − 4y = −27 and x − 2y = −11 →
  6. 6.2x + 5y = 27 and 5x + 2y = −6 →
  7. 7.4x + 3y = 17 and 3x + 3y = 18 →
  8. 8.x − y = 7 and 2x − 5y = 11 →
  9. 9.7x + 4y = 28 and 4x + 7y = −17 →
  10. 10.5x + 4y = 46 and 3x − y = 14 →
  11. 11.4x + y = 38 and x + 4y = 32 →
  12. 12.5x + 7y = −19 and 7x + 5y = −41 →
  13. 13.3x + 8y = 67 and 8x + 3y = 32 →
  14. 14.5x + 5y = 45 and 4x + 2y = 24 →
  15. 15.2x − y = 0 and 5x − 5y = −10 →
  16. 16.6x + 4y = −26 and x − 4y = 33 →
  17. 17.6x − 3y = −9 and 6x − 2y = 0 →
  18. 18.6x − 5y = −2 and 4x + y = −36 →
  19. 19.6x − 4y = −14 and 2x + y = 14 →
  20. 20.x + 2y = 7 and 6x + 6y = 24 →
  21. 21.2x + 9y = −31 and 9x + 2y = −24 →
  22. 22.4x + 4y = 28 and 3x + 5y = 23 →
  23. 23.x + 2y = 2 and x − 3y = 7 →
  24. 24.4x + 4y = −52 and 2x + y = −18 →
  25. 25.x + y = −6 and 4x − 2y = 24 →
  26. 26.6x + 4y = −32 and 4x + 6y = −28 →
  27. 27.4x + y = −11 and x + 4y = −14 →
  28. 28.4x + 3y = −31 and 6x + 5y = −47 →
  29. 29.x − y = −1 and 5x − 2y = 1 →
  30. 30.7x + 4y = −30 and 4x + 7y = −36 →
  31. 31.6x + 6y = 24 and 5x + 3y = 16 →
  32. 32.5x + 5y = −10 and 3x − y = −30 →
  33. 33.7x + 6y = −55 and 6x + 7y = −62 →
  34. 34.5x − 6y = −75 and 6x + 2y = −44 →
  35. 35.2x − 2y = −12 and x + y = 8 →
  36. 36.8x + 6y = 14 and 6x + 8y = 14 →
  37. 37.5x + 4y = −13 and 4x + 5y = −23 →
  38. 38.2x + 6y = 20 and 2x + y = 15 →
  39. 39.3x − y = 19 and 5x + y = 29 →
  40. 40.x + 2y = 23 and x + 5y = 47 →

Answer key

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

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