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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 274 · 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 + 3y = −24 and 5x − 5y = −10 →
  2. 2.6x + 4y = −18 and 4x + y = −27 →
  3. 3.x − 2y = 1 and 6x + 2y = 62 →
  4. 4.5x + y = −29 and 5x − 3y = −53 →
  5. 5.x + y = 2 and x − y = 14 →
  6. 6.6x + 2y = 30 and x + 5y = 33 →
  7. 7.9x + y = 67 and x + 9y = 43 →
  8. 8.9x + y = −13 and x + 9y = −37 →
  9. 9.x − 6y = 53 and 5x − y = 4 →
  10. 10.5x + 4y = 76 and 6x − 6y = −6 →
  11. 11.x + 4y = 30 and 4x + y = 15 →
  12. 12.x − 5y = −44 and x + 4y = 37 →
  13. 13.2x + 2y = 16 and x − y = 2 →
  14. 14.6x + 4y = 4 and 4x + 6y = 26 →
  15. 15.x + 9y = 59 and 9x + y = 51 →
  16. 16.5x + 2y = −3 and 6x − 3y = −36 →
  17. 17.4x − 3y = 19 and 3x − 5y = 6 →
  18. 18.x + 2y = 7 and x + 3y = 9 →
  19. 19.2x + 2y = 14 and x + 4y = 16 →
  20. 20.4x + y = −17 and x + 4y = −8 →
  21. 21.5x + 9y = 31 and 9x + 5y = 11 →
  22. 22.6x + 4y = 22 and 5x + 2y = 17 →
  23. 23.5x − 4y = −11 and 6x − y = 2 →
  24. 24.2x + 3y = 1 and 6x + 5y = 7 →
  25. 25.x + 2y = 0 and 2x + y = 6 →
  26. 26.x + 3y = −9 and 3x + y = 21 →
  27. 27.6x + y = 44 and 3x + 2y = 25 →
  28. 28.5x − 3y = 18 and 6x − 3y = 21 →
  29. 29.3x + 3y = 30 and 2x + 5y = 23 →
  30. 30.5x − 3y = −21 and x + 6y = 9 →
  31. 31.6x + 5y = 19 and x + 4y = 19 →
  32. 32.2x + 6y = 44 and x − y = −2 →
  33. 33.8x + 2y = 34 and 2x + 8y = 76 →
  34. 34.7x + 4y = −22 and 4x + 7y = 11 →
  35. 35.x − 3y = 22 and 2x + y = 9 →
  36. 36.7x + y = 20 and x + 7y = 44 →
  37. 37.4x − 6y = 0 and 5x + y = 17 →
  38. 38.5x + 3y = 39 and 4x − 5y = −28 →
  39. 39.5x + 3y = 34 and 3x + 5y = 46 →
  40. 40.5x − 4y = −33 and 4x + 3y = 17 →

Answer key

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

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