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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 166 · 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. 1.3x − 6y = −21 and 3x + 2y = −5 →
  2. 2.3x + 2y = 35 and 2x + 3y = 35 →
  3. 3.3x − 5y = 1 and 6x − y = 11 →
  4. 4.5x − y = 1 and 4x + 5y = 53 →
  5. 5.5x + y = −44 and 6x − y = −33 →
  6. 6.5x + 5y = 35 and 2x + 6y = 30 →
  7. 7.x + 9y = 75 and 9x + y = −45 →
  8. 8.2x + 3y = 25 and 5x + 3y = 22 →
  9. 9.x + 3y = 18 and 2x + 2y = 8 →
  10. 10.4x + 2y = −36 and 5x + 5y = −65 →
  11. 11.9x + 3y = 69 and 3x + 9y = 63 →
  12. 12.4x + 6y = 56 and 3x − 5y = −15 →
  13. 13.4x − 5y = −6 and 2x + 2y = 6 →
  14. 14.6x − 2y = 32 and 6x − 4y = 46 →
  15. 15.3x + 5y = 48 and 4x + 2y = 22 →
  16. 16.9x + 5y = 52 and 5x + 9y = 60 →
  17. 17.5x − 4y = −77 and 5x + 5y = −5 →
  18. 18.9x + 3y = 33 and 3x + 9y = 51 →
  19. 19.x − 3y = 26 and 4x + 5y = −15 →
  20. 20.5x − y = −38 and 3x − 4y = −33 →
  21. 21.6x − 2y = 32 and 2x + 4y = −8 →
  22. 22.2x − 4y = 22 and x + 4y = 5 →
  23. 23.9x + 5y = 54 and 5x + 9y = 86 →
  24. 24.6x − 4y = 32 and 6x + 5y = 14 →
  25. 25.4x + 4y = −16 and x − 2y = 2 →
  26. 26.3x − 5y = −3 and 4x + 4y = −36 →
  27. 27.6x − 3y = −6 and 2x + y = 14 →
  28. 28.5x − y = −52 and 3x − 3y = −48 →
  29. 29.x + 4y = −20 and 4x + y = 10 →
  30. 30.5x − 5y = −5 and 6x + 6y = 66 →
  31. 31.9x + 8y = 128 and 8x + 9y = 127 →
  32. 32.6x + 8y = −2 and 8x + 6y = 16 →
  33. 33.6x + 6y = 48 and 4x − 4y = −16 →
  34. 34.4x − 4y = −36 and x + 6y = 19 →
  35. 35.3x + 5y = −22 and 5x − y = −46 →
  36. 36.x + 3y = 18 and x − 5y = −38 →
  37. 37.2x − y = −9 and 2x + y = −11 →
  38. 38.3x + 6y = 42 and 2x + 3y = 20 →
  39. 39.9x + 4y = 53 and 4x + 9y = −27 →
  40. 40.4x + y = 17 and 5x + y = 19 →

Answer key

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

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