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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 142 · 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 = −6 and 3x + y = 15 →
  2. 2.3x + 3y = 21 and x − 2y = −5 →
  3. 3.4x + y = 2 and x + 4y = −7 →
  4. 4.2x + 4y = 12 and 4x + 2y = 18 →
  5. 5.4x + 5y = −29 and 5x + 4y = −16 →
  6. 6.6x + 3y = −3 and 4x + 4y = 4 →
  7. 7.7x + 8y = 2 and 8x + 7y = −2 →
  8. 8.4x + 9y = −33 and 9x + 4y = −58 →
  9. 9.x − 3y = −17 and 2x − y = 6 →
  10. 10.6x + y = −47 and x + 6y = −37 →
  11. 11.8x + y = 0 and x + 8y = 63 →
  12. 12.x − 2y = −22 and 5x + y = −11 →
  13. 13.4x + 6y = 16 and x − 2y = 11 →
  14. 14.3x − 5y = −37 and 2x − 5y = −28 →
  15. 15.2x + 6y = 46 and 6x − 6y = −6 →
  16. 16.3x + 2y = −11 and 6x + 2y = −20 →
  17. 17.4x + 4y = 4 and 6x + 3y = −3 →
  18. 18.2x − 4y = −8 and 5x + y = 35 →
  19. 19.4x − 2y = 44 and x − 2y = 17 →
  20. 20.2x − y = −8 and x − y = −6 →
  21. 21.2x + 3y = 21 and 3x + y = 21 →
  22. 22.x + 6y = 15 and 2x + 2y = 20 →
  23. 23.9x + y = 26 and x + 9y = 74 →
  24. 24.3x + 5y = 37 and 5x + 6y = 50 →
  25. 25.2x − 2y = 0 and 2x + y = 18 →
  26. 26.6x − y = 41 and x + 2y = 22 →
  27. 27.x + 5y = −16 and 6x + 6y = 0 →
  28. 28.4x + y = 0 and 3x + y = 1 →
  29. 29.x + 5y = −2 and 5x + 3y = 12 →
  30. 30.3x + 3y = 24 and 6x + y = 38 →
  31. 31.4x + 2y = −32 and 2x + 4y = −10 →
  32. 32.6x + 2y = 66 and x + 2y = 26 →
  33. 33.8x + 5y = 37 and 5x + 8y = 67 →
  34. 34.2x − 4y = −26 and 2x + y = 14 →
  35. 35.x − 6y = 37 and 4x + 2y = 18 →
  36. 36.x + 4y = −10 and 4x − 2y = −4 →
  37. 37.5x + 6y = 2 and 4x + 4y = 0 →
  38. 38.2x + 5y = 23 and 4x + 3y = −3 →
  39. 39.2x + 6y = 10 and 4x + 5y = 13 →
  40. 40.2x + y = −7 and 6x + 5y = −39 →

Answer key

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

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