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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 554 · 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 = 14 and 5x − 2y = 40 →
  2. 2.6x + y = −43 and 6x − 2y = −40 →
  3. 3.9x + 2y = 41 and 2x + 9y = −8 →
  4. 4.6x + y = 26 and 5x − 4y = 12 →
  5. 5.6x + 2y = 20 and 2x + 6y = −4 →
  6. 6.9x + 5y = −47 and 5x + 9y = 5 →
  7. 7.3x + y = −21 and 4x − 4y = 4 →
  8. 8.4x + 7y = −42 and 7x + 4y = −57 →
  9. 9.9x + 2y = −11 and 2x + 9y = 66 →
  10. 10.2x + 9y = 41 and 9x + 2y = 69 →
  11. 11.6x + 3y = 66 and 4x + y = 38 →
  12. 12.2x − 6y = 34 and 4x + y = 3 →
  13. 13.2x + y = 4 and 3x + 4y = −4 →
  14. 14.3x + 6y = 36 and 6x + 3y = 54 →
  15. 15.2x + 5y = −3 and 2x − y = 15 →
  16. 16.6x − 6y = −36 and 4x + 6y = 6 →
  17. 17.3x − 6y = −42 and x + y = 10 →
  18. 18.5x + 5y = −10 and x + 6y = −42 →
  19. 19.x + 3y = 22 and 4x − 6y = −38 →
  20. 20.2x + 4y = 6 and 4x − 4y = 36 →
  21. 21.2x + 5y = 35 and 5x + 2y = −7 →
  22. 22.4x − y = 20 and 3x + 3y = 45 →
  23. 23.2x + y = 10 and 6x + 4y = 34 →
  24. 24.x + 4y = 12 and 6x − 6y = 12 →
  25. 25.x + 9y = 42 and 9x + y = 58 →
  26. 26.6x + 3y = −33 and 2x − 4y = −16 →
  27. 27.9x + 8y = 63 and 8x + 9y = 73 →
  28. 28.4x − 4y = −52 and 2x + 4y = 22 →
  29. 29.4x − 6y = −2 and 6x − 3y = 15 →
  30. 30.2x + y = 20 and 4x − y = 22 →
  31. 31.x − y = 15 and 4x − 3y = 52 →
  32. 32.8x + 7y = 93 and 7x + 8y = 87 →
  33. 33.2x + 8y = 82 and 8x + 2y = 88 →
  34. 34.x + 6y = −19 and x − 4y = 1 →
  35. 35.3x + 8y = −45 and 8x + 3y = −10 →
  36. 36.8x + 2y = 58 and 2x + 8y = 82 →
  37. 37.3x − 3y = −12 and 2x + 5y = 55 →
  38. 38.5x + y = −12 and 3x − 6y = −27 →
  39. 39.2x + 8y = 22 and 8x + 2y = −32 →
  40. 40.3x − 6y = −6 and 6x − 4y = 20 →

Answer key

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

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