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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 380 · 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. 1.2x − 2y = 12 and 5x + y = 6 →
  2. 2.5x + 5y = −20 and x + 5y = −28 →
  3. 3.2x − y = 11 and x + 2y = 3 →
  4. 4.4x + 5y = 58 and 3x + 6y = 57 →
  5. 5.9x + 3y = 63 and 3x + 9y = 93 →
  6. 6.4x − 5y = −9 and 4x − 3y = 1 →
  7. 7.3x − 5y = 30 and 2x + 6y = −8 →
  8. 8.x + y = 15 and 6x + 5y = 83 →
  9. 9.6x − 6y = 42 and 4x + 4y = 36 →
  10. 10.3x + 4y = −17 and 2x + 5y = −30 →
  11. 11.6x − 3y = 27 and 4x − 6y = −18 →
  12. 12.5x + y = 44 and x + 5y = 4 →
  13. 13.x + 9y = 77 and 9x + y = −27 →
  14. 14.3x + 2y = 20 and 2x + 3y = 20 →
  15. 15.6x + 3y = −9 and 3x + 6y = 27 →
  16. 16.x + 5y = 36 and 3x + 3y = 36 →
  17. 17.6x + 4y = 30 and 4x + 6y = 30 →
  18. 18.3x − 4y = 19 and 3x + 6y = 9 →
  19. 19.9x + 8y = 41 and 8x + 9y = 44 →
  20. 20.4x − 6y = −2 and 2x − 5y = −3 →
  21. 21.5x − 2y = −17 and 4x + 2y = −28 →
  22. 22.2x + 5y = −33 and 5x + 6y = −37 →
  23. 23.9x + 2y = 50 and 2x + 9y = −6 →
  24. 24.3x − 2y = 5 and 6x + 4y = −22 →
  25. 25.3x − 5y = 48 and 2x + y = 6 →
  26. 26.3x − y = 1 and 3x + y = 5 →
  27. 27.6x + 5y = −16 and 5x + 3y = −4 →
  28. 28.x − 6y = −33 and 6x + 3y = 75 →
  29. 29.4x + 8y = 60 and 8x + 4y = 72 →
  30. 30.5x + 5y = −5 and x + 2y = −8 →
  31. 31.x + 4y = −6 and 4x + y = 21 →
  32. 32.x + 7y = 48 and 7x + y = −48 →
  33. 33.3x − 4y = −38 and 5x + 2y = −20 →
  34. 34.6x + 4y = −28 and 4x + 3y = −19 →
  35. 35.6x + 2y = 44 and 2x + 6y = 20 →
  36. 36.2x + 3y = 18 and 3x + y = −1 →
  37. 37.4x − 5y = −16 and 6x + 2y = 52 →
  38. 38.5x + 3y = 11 and x + 4y = −8 →
  39. 39.4x + 5y = 38 and 4x + 2y = 20 →
  40. 40.2x + 8y = 66 and 8x + 2y = 84 →

Answer key

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

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