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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 558 · 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.x + y = 7 and 3x − 6y = 3 →
  2. 2.9x + 4y = 34 and 4x + 9y = 44 →
  3. 3.4x + y = −19 and x + 4y = −31 →
  4. 4.x + 4y = 12 and 4x + y = 18 →
  5. 5.4x − 5y = 37 and 2x + 5y = −19 →
  6. 6.5x + y = 18 and 3x + y = 14 →
  7. 7.5x + 9y = 69 and 9x + 5y = 57 →
  8. 8.7x + 9y = −47 and 9x + 7y = −33 →
  9. 9.2x + 5y = 9 and 5x − 2y = 37 →
  10. 10.2x + y = 19 and x + y = 12 →
  11. 11.3x + y = −21 and 5x + 4y = −28 →
  12. 12.5x − 4y = 13 and 6x + 3y = 0 →
  13. 13.6x + 6y = −18 and 2x − 6y = 58 →
  14. 14.4x + 3y = 26 and 2x + 2y = 12 →
  15. 15.9x + 4y = 54 and 4x + 9y = 89 →
  16. 16.6x − 2y = −28 and 4x + 6y = −48 →
  17. 17.3x + 8y = −2 and 8x + 3y = −42 →
  18. 18.4x + 9y = −67 and 9x + 4y = −37 →
  19. 19.x + 4y = −25 and 4x + y = −40 →
  20. 20.8x + 4y = −44 and 4x + 8y = −52 →
  21. 21.3x + 6y = 39 and 6x − 4y = −66 →
  22. 22.3x + 3y = 30 and 5x − 4y = 5 →
  23. 23.3x + y = −1 and 2x + 3y = 18 →
  24. 24.5x − 5y = −5 and 5x − 6y = −9 →
  25. 25.x + 5y = 19 and 3x + 3y = 21 →
  26. 26.x + 4y = 41 and 4x + y = 29 →
  27. 27.4x − 2y = 2 and 6x − 2y = 4 →
  28. 28.6x + 3y = −15 and x + 3y = 0 →
  29. 29.4x + y = 4 and x + 4y = −29 →
  30. 30.8x + 9y = −100 and 9x + 8y = −104 →
  31. 31.3x + 2y = −24 and 2x + 5y = −27 →
  32. 32.3x + 4y = 26 and 6x + 2y = 4 →
  33. 33.8x + 9y = 25 and 9x + 8y = 26 →
  34. 34.x + 3y = 12 and x + y = −2 →
  35. 35.4x + 6y = −26 and 6x + 6y = −42 →
  36. 36.3x + 2y = −39 and 5x + 4y = −69 →
  37. 37.2x + 2y = 12 and 6x + y = 26 →
  38. 38.4x + 6y = −66 and 3x + 6y = −63 →
  39. 39.5x + 5y = 70 and 5x − 3y = 30 →
  40. 40.5x + y = −21 and 2x + 2y = 6 →

Answer key

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

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