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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 213 · 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. 1.8x + y = −15 and x + 8y = 6 →
  2. 2.3x + y = −2 and x + 4y = 14 →
  3. 3.7x + 8y = 58 and 8x + 7y = 62 →
  4. 4.2x − 6y = −32 and 2x + 5y = 56 →
  5. 5.2x + 4y = 22 and 4x + 2y = 2 →
  6. 6.5x + 8y = −33 and 8x + 5y = −45 →
  7. 7.6x − 5y = 27 and 2x + 4y = −8 →
  8. 8.9x + y = 26 and x + 9y = −6 →
  9. 9.5x + 3y = 42 and 6x + 2y = 52 →
  10. 10.2x − 6y = 2 and 3x − 4y = −12 →
  11. 11.2x + 3y = 31 and 3x + 2y = 24 →
  12. 12.2x + 4y = 38 and 6x + 4y = 74 →
  13. 13.8x + 7y = 65 and 7x + 8y = 70 →
  14. 14.3x + 6y = −30 and 5x + 6y = −18 →
  15. 15.4x + 3y = 42 and 3x + 4y = 42 →
  16. 16.5x + 6y = −34 and 3x + 5y = −19 →
  17. 17.2x + y = 10 and x + 2y = 11 →
  18. 18.9x + 5y = 31 and 5x + 9y = 67 →
  19. 19.4x + 2y = 4 and 5x + y = 14 →
  20. 20.5x + 6y = −33 and 5x + y = −43 →
  21. 21.5x + 4y = −11 and 6x + y = 2 →
  22. 22.3x − 5y = 6 and 2x − 3y = 5 →
  23. 23.4x + y = 24 and x + 4y = 36 →
  24. 24.5x − 2y = −11 and x − y = −4 →
  25. 25.3x + 5y = 61 and x + 4y = 39 →
  26. 26.5x + 6y = 69 and 6x + 5y = 63 →
  27. 27.2x + 4y = 34 and 3x + 4y = 39 →
  28. 28.x + 2y = −1 and 2x + y = 13 →
  29. 29.3x + 2y = 13 and 6x − y = 16 →
  30. 30.5x + 2y = −5 and 5x + 5y = −20 →
  31. 31.5x + 4y = 32 and 4x + 5y = 22 →
  32. 32.2x + 6y = 16 and x + 2y = 7 →
  33. 33.4x − 3y = 15 and x + 2y = 23 →
  34. 34.5x − 2y = 16 and x + y = 6 →
  35. 35.x + 4y = 14 and 4x + 6y = 26 →
  36. 36.4x + 7y = −55 and 7x + 4y = −22 →
  37. 37.6x + 4y = 6 and 2x + 5y = 13 →
  38. 38.6x − 4y = 26 and 4x + 3y = 23 →
  39. 39.x − 4y = −21 and 3x + 2y = −7 →
  40. 40.x + 4y = 19 and 2x + 3y = 18 →

Answer key

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

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