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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 914 · 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 + 8y = −20 and 8x + 2y = 10 →
  2. 2.5x + y = 6 and x + y = −2 →
  3. 3.3x − 3y = −27 and 5x + 4y = 18 →
  4. 4.x + 2y = 3 and 5x − 6y = −65 →
  5. 5.5x + 4y = 30 and x + 3y = 17 →
  6. 6.6x − 2y = −34 and x + 4y = −23 →
  7. 7.5x + 5y = −50 and 3x + 2y = −21 →
  8. 8.2x + 6y = 36 and x + y = 10 →
  9. 9.x − 5y = −27 and 2x − 2y = −6 →
  10. 10.2x − 4y = −22 and 2x − 6y = −30 →
  11. 11.6x + 7y = −85 and 7x + 6y = −84 →
  12. 12.2x + 4y = 6 and 4x − 2y = −28 →
  13. 13.9x + 7y = −40 and 7x + 9y = −24 →
  14. 14.x + 3y = 16 and 5x + 6y = 35 →
  15. 15.9x + 4y = −32 and 4x + 9y = −7 →
  16. 16.2x − y = 6 and 4x + 3y = −8 →
  17. 17.x + 2y = −5 and 4x + y = 1 →
  18. 18.5x + 5y = −35 and 2x − 5y = 7 →
  19. 19.5x + 8y = 32 and 8x + 5y = 59 →
  20. 20.3x − 3y = −6 and 2x + 4y = 20 →
  21. 21.2x + 6y = −12 and 3x − y = 22 →
  22. 22.9x + 4y = −32 and 4x + 9y = −7 →
  23. 23.5x + 6y = −27 and 4x + y = 5 →
  24. 24.4x + 3y = 48 and 3x + 4y = 50 →
  25. 25.4x + 2y = −14 and 5x + y = −10 →
  26. 26.6x + 3y = −3 and 3x + 6y = −42 →
  27. 27.2x + 4y = 26 and 2x + 6y = 36 →
  28. 28.4x + 3y = −28 and 3x + 4y = −35 →
  29. 29.x + 2y = 5 and 3x − 3y = 6 →
  30. 30.6x − 4y = 24 and x − 3y = −3 →
  31. 31.2x + 5y = 1 and 5x + 5y = 10 →
  32. 32.4x + 9y = −1 and 9x + 4y = 14 →
  33. 33.6x + 2y = 46 and 2x + 6y = 10 →
  34. 34.2x + 6y = −8 and 3x + 6y = −3 →
  35. 35.4x − y = −4 and 4x + 2y = 20 →
  36. 36.8x + 3y = 33 and 3x + 8y = 33 →
  37. 37.7x + 6y = −50 and 6x + 7y = −41 →
  38. 38.2x − 6y = 16 and x + 5y = −8 →
  39. 39.8x + 9y = 145 and 9x + 8y = 144 →
  40. 40.5x + y = 27 and x − 4y = −3 →

Answer key

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

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