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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 399 · 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. 1.5x + 2y = 46 and 5x + 6y = 58 →
  2. 2.7x + 2y = −29 and 2x + 7y = 11 →
  3. 3.5x − 4y = 7 and 6x + 6y = 30 →
  4. 4.5x + 2y = −27 and 2x + 5y = 6 →
  5. 5.4x + 7y = 32 and 7x + 4y = 23 →
  6. 6.x + 6y = 54 and 6x + y = 44 →
  7. 7.2x + 4y = 20 and 4x + 2y = 22 →
  8. 8.9x + 7y = 37 and 7x + 9y = 43 →
  9. 9.7x + 3y = 39 and 3x + 7y = 51 →
  10. 10.6x + 4y = 42 and 2x − 2y = −16 →
  11. 11.8x + 6y = −14 and 6x + 8y = −28 →
  12. 12.x + y = 7 and 2x − 5y = −7 →
  13. 13.x + 9y = 12 and 9x + y = 28 →
  14. 14.6x + 5y = 1 and 5x + y = −15 →
  15. 15.6x + 9y = 15 and 9x + 6y = 0 →
  16. 16.3x − 3y = 12 and x + 6y = −10 →
  17. 17.6x + 3y = −3 and 2x + 6y = −36 →
  18. 18.6x − 4y = −28 and 4x + 2y = −42 →
  19. 19.2x − y = −10 and 4x + 5y = 36 →
  20. 20.3x + 3y = 0 and 4x + 5y = −6 →
  21. 21.2x + 7y = 71 and 7x + 2y = 46 →
  22. 22.6x + 4y = 80 and 4x + 6y = 80 →
  23. 23.3x + 7y = 10 and 7x + 3y = 50 →
  24. 24.4x + 8y = 0 and 8x + 4y = −12 →
  25. 25.4x + 6y = −60 and 6x + 4y = −70 →
  26. 26.3x + y = 20 and 5x − 2y = 15 →
  27. 27.5x + y = −9 and 3x − y = 1 →
  28. 28.2x − y = −23 and 6x − 6y = −96 →
  29. 29.5x + y = −44 and 6x + y = −53 →
  30. 30.3x + 3y = 33 and 5x − 4y = 1 →
  31. 31.3x − 2y = −32 and 3x + y = −20 →
  32. 32.3x + y = 36 and 5x + 2y = 63 →
  33. 33.5x − 4y = 10 and 3x + 2y = 28 →
  34. 34.6x − 3y = 9 and x − 2y = 12 →
  35. 35.2x − y = −13 and x + 3y = 25 →
  36. 36.4x − 2y = 4 and x − y = 3 →
  37. 37.4x + 3y = −10 and 6x − 3y = 30 →
  38. 38.4x − 5y = −32 and 2x + 5y = 44 →
  39. 39.x + 4y = 9 and 4x + y = 6 →
  40. 40.4x + 4y = −4 and 6x + 5y = −9 →

Answer key

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

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