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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 773 · 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. 1.6x + y = 3 and x + 6y = −17 →
  2. 2.3x + 3y = 33 and x − 2y = 2 →
  3. 3.x + 7y = −38 and 7x + y = 22 →
  4. 4.x + y = 7 and 3x − 5y = 13 →
  5. 5.4x + 5y = −45 and 6x + 5y = −55 →
  6. 6.x + 7y = 26 and 7x + y = 38 →
  7. 7.x − 3y = −22 and 3x + y = −6 →
  8. 8.6x + 5y = 44 and 4x + 3y = 28 →
  9. 9.3x + y = −33 and x + 3y = −27 →
  10. 10.6x + 6y = 36 and x − y = −10 →
  11. 11.5x + 4y = 28 and 2x + y = 10 →
  12. 12.2x + 3y = 13 and 2x − y = 1 →
  13. 13.3x + 8y = 17 and 8x + 3y = 27 →
  14. 14.6x + 7y = −89 and 7x + 6y = −93 →
  15. 15.x + y = 8 and 3x − y = 4 →
  16. 16.5x − 2y = 38 and x + 4y = −32 →
  17. 17.5x + 3y = −25 and x − 3y = 13 →
  18. 18.7x + 4y = −6 and 4x + 7y = −27 →
  19. 19.6x − 6y = 24 and 5x + y = −10 →
  20. 20.6x + 5y = 75 and 4x − 3y = −7 →
  21. 21.3x + 2y = 45 and 2x + 3y = 45 →
  22. 22.6x + y = −25 and 2x − 5y = 29 →
  23. 23.3x + 4y = 30 and 2x − 6y = −58 →
  24. 24.6x + y = 0 and 2x − y = 8 →
  25. 25.7x + 5y = −9 and 5x + 7y = −3 →
  26. 26.6x − 2y = 68 and 3x + y = 20 →
  27. 27.6x + y = 27 and 2x + 3y = 1 →
  28. 28.5x + 6y = 28 and 3x − 5y = 34 →
  29. 29.2x + y = 21 and x + 2y = 21 →
  30. 30.x − 2y = 9 and 5x + 3y = 6 →
  31. 31.x + y = 7 and x − y = −1 →
  32. 32.x + 2y = 20 and 4x − 6y = −46 →
  33. 33.4x + 6y = 40 and 6x + 6y = 54 →
  34. 34.4x + 4y = 0 and 6x − 5y = 33 →
  35. 35.5x − y = 50 and 3x + y = 22 →
  36. 36.x + 5y = 19 and x − 3y = −13 →
  37. 37.5x + 4y = 11 and 4x + 4y = 4 →
  38. 38.x + 7y = 26 and 7x + y = −58 →
  39. 39.4x + 5y = 54 and 3x + 2y = 30 →
  40. 40.5x + 3y = 12 and 3x + 5y = −12 →

Answer key

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

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