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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 202 · 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 + 8y = 32 and 8x + 3y = −43 →
  2. 2.x − 5y = −18 and x + 6y = 26 →
  3. 3.2x − 3y = −38 and 2x − 5y = −54 →
  4. 4.6x + y = 28 and 2x + 3y = 4 →
  5. 5.x + 2y = 25 and 2x + y = 23 →
  6. 6.2x − 5y = 20 and x − 4y = 19 →
  7. 7.2x + 2y = −16 and 4x + 5y = −37 →
  8. 8.9x + 3y = −6 and 3x + 9y = 6 →
  9. 9.3x + 4y = 34 and 4x + 4y = 40 →
  10. 10.x − 5y = −23 and 6x + 6y = 42 →
  11. 11.x − 2y = 11 and 6x + 5y = −70 →
  12. 12.4x + 6y = 54 and 3x − 3y = 18 →
  13. 13.2x − y = −6 and 5x − 6y = 13 →
  14. 14.x + 2y = 24 and 4x + y = 33 →
  15. 15.x + 2y = 7 and x − 5y = −21 →
  16. 16.2x − 4y = −26 and 4x − 6y = −44 →
  17. 17.4x + 6y = 18 and 5x + 4y = 5 →
  18. 18.2x + y = −1 and x + 2y = 7 →
  19. 19.2x + 3y = −16 and x + 4y = −18 →
  20. 20.6x + 2y = 48 and 3x − 4y = −6 →
  21. 21.x + y = −13 and 5x − y = −23 →
  22. 22.4x − 2y = −4 and x + 6y = 38 →
  23. 23.4x + y = 43 and x + 5y = 44 →
  24. 24.2x − 6y = 46 and x + 2y = −22 →
  25. 25.x + 5y = 8 and 5x + y = 16 →
  26. 26.x + 6y = 29 and 6x + 2y = 38 →
  27. 27.4x + 4y = 16 and 4x + 6y = 12 →
  28. 28.2x − 3y = −29 and 6x + 6y = 48 →
  29. 29.4x + 2y = 30 and 4x − 5y = 51 →
  30. 30.x + 6y = 43 and 6x + y = 13 →
  31. 31.5x + 2y = −19 and 4x + 5y = −22 →
  32. 32.9x + y = 13 and x + 9y = −43 →
  33. 33.5x + 7y = 2 and 7x + 5y = −2 →
  34. 34.5x + 3y = −8 and x + 2y = 11 →
  35. 35.9x + 5y = 14 and 5x + 9y = −42 →
  36. 36.5x + 4y = −25 and 6x − y = −59 →
  37. 37.3x + 2y = −10 and 4x + 6y = −20 →
  38. 38.9x + 8y = 14 and 8x + 9y = 20 →
  39. 39.6x + 5y = 14 and 3x + 3y = 6 →
  40. 40.4x + 5y = −26 and 2x + 5y = −8 →

Answer key

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

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