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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 33 · 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. 1.4x + 2y = 0 and 3x + 5y = −14 →
  2. 2.2x + 6y = 34 and x − 4y = −18 →
  3. 3.9x + 2y = 56 and 2x + 9y = −56 →
  4. 4.3x + 5y = −28 and 5x + 3y = −36 →
  5. 5.x + 7y = 22 and 7x + y = 10 →
  6. 6.2x + 3y = 6 and 3x + 3y = 12 →
  7. 7.7x + 5y = −46 and 5x + 7y = −26 →
  8. 8.4x − 3y = −23 and 3x + 4y = 39 →
  9. 9.x + 5y = −44 and 5x + 4y = −31 →
  10. 10.4x + 4y = 40 and 5x − 3y = 10 →
  11. 11.x + 3y = 0 and 6x + 4y = 28 →
  12. 12.3x − 4y = −20 and 6x + 2y = −20 →
  13. 13.5x + 6y = −35 and 5x + 2y = −15 →
  14. 14.5x + y = 9 and x + 5y = 21 →
  15. 15.x + 4y = 37 and 2x + 2y = 26 →
  16. 16.4x + 9y = 33 and 9x + 4y = 58 →
  17. 17.x + 4y = −13 and 4x + y = 23 →
  18. 18.3x − y = 10 and 4x − 4y = −8 →
  19. 19.2x + 4y = 18 and 2x − y = −2 →
  20. 20.x − 5y = −19 and 2x + 2y = 22 →
  21. 21.2x + y = 17 and x − 2y = 1 →
  22. 22.5x + 4y = 73 and 5x − 6y = 3 →
  23. 23.6x − 5y = −57 and x − 3y = −16 →
  24. 24.4x + y = 34 and x + 4y = 16 →
  25. 25.3x + 5y = 13 and 6x + 6y = 30 →
  26. 26.4x + y = −12 and x + 4y = 27 →
  27. 27.3x + 2y = 34 and x + 5y = 33 →
  28. 28.7x + y = −12 and x + 7y = 12 →
  29. 29.3x + 8y = 29 and 8x + 3y = 59 →
  30. 30.2x + 3y = −11 and x + 3y = −19 →
  31. 31.6x + y = −16 and 3x − 2y = −28 →
  32. 32.3x + 2y = −33 and 6x − 5y = 15 →
  33. 33.3x + 5y = −50 and 5x + 6y = −67 →
  34. 34.9x + 3y = 30 and 3x + 9y = 66 →
  35. 35.8x + 4y = 76 and 4x + 8y = 56 →
  36. 36.4x − 3y = 17 and x + 2y = 7 →
  37. 37.8x + 3y = −28 and 3x + 8y = −38 →
  38. 38.9x + 2y = 90 and 2x + 9y = 97 →
  39. 39.9x + 7y = −117 and 7x + 9y = −123 →
  40. 40.5x + 5y = −60 and 3x + 4y = −39 →

Answer key

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

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