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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 121 · 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. 1.9x + y = −38 and x + 9y = 58 →
  2. 2.5x + 3y = −20 and 3x + 5y = 4 →
  3. 3.x + 6y = 44 and 2x + 3y = 34 →
  4. 4.4x + 4y = −28 and x + 5y = 1 →
  5. 5.6x + 4y = 34 and 4x + 6y = 26 →
  6. 6.4x + y = −14 and 5x + y = −19 →
  7. 7.3x + 6y = 33 and 2x + 2y = 14 →
  8. 8.7x + 8y = 18 and 8x + 7y = 27 →
  9. 9.6x + y = −26 and x + 6y = −51 →
  10. 10.6x − 2y = 36 and x + 6y = −13 →
  11. 11.4x − 4y = 4 and x − 3y = 19 →
  12. 12.4x + y = −33 and x − 6y = 23 →
  13. 13.x + 2y = −7 and 3x − 4y = 29 →
  14. 14.6x + 6y = −90 and 5x − 3y = −3 →
  15. 15.x − 3y = 4 and 6x − 5y = −2 →
  16. 16.4x + y = −45 and 5x + 2y = −63 →
  17. 17.6x + 2y = −24 and 2x + 6y = −24 →
  18. 18.6x + 8y = −38 and 8x + 6y = −32 →
  19. 19.4x + 4y = −28 and 4x − 4y = −44 →
  20. 20.6x + 5y = 41 and 4x − 3y = −17 →
  21. 21.5x + 4y = 52 and 5x + 6y = 58 →
  22. 22.x − 3y = −1 and x + 5y = 7 →
  23. 23.2x + 3y = 4 and 3x + 2y = 11 →
  24. 24.6x − 6y = −48 and 4x − 6y = −50 →
  25. 25.x + 5y = −2 and 3x + 4y = 5 →
  26. 26.3x + 2y = 5 and 6x + 3y = 9 →
  27. 27.5x − 2y = −22 and x + 4y = 22 →
  28. 28.5x + 2y = 38 and 3x − 2y = −6 →
  29. 29.4x − 4y = 44 and 3x + y = −3 →
  30. 30.x + 6y = 20 and 6x + y = 15 →
  31. 31.4x + 5y = −38 and x + y = −9 →
  32. 32.6x + 2y = 24 and 5x + 4y = 27 →
  33. 33.2x + 5y = 29 and 5x − 3y = −67 →
  34. 34.x + 5y = 22 and 2x − 2y = −28 →
  35. 35.2x + 4y = 18 and x + 6y = 13 →
  36. 36.5x + y = 11 and x + 5y = −41 →
  37. 37.4x − 5y = 56 and x + y = −4 →
  38. 38.2x − y = 3 and x − 4y = −2 →
  39. 39.2x + 5y = 45 and 6x − y = 23 →
  40. 40.x + 3y = 5 and 3x + y = −17 →

Answer key

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

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