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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 366 · 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 + 4y = −11 and 6x − 6y = 90 →
  2. 2.2x + y = 20 and x + 2y = 13 →
  3. 3.x + 4y = −35 and 2x + 2y = −22 →
  4. 4.2x + 3y = 20 and 4x + 2y = 16 →
  5. 5.3x + 2y = 0 and x + 2y = −12 →
  6. 6.5x + 9y = −72 and 9x + 5y = −96 →
  7. 7.5x − 3y = 49 and x − 5y = 45 →
  8. 8.2x + 8y = 2 and 8x + 2y = −22 →
  9. 9.5x − 2y = 23 and 3x + 3y = −3 →
  10. 10.x − 4y = −14 and 3x − 2y = −2 →
  11. 11.4x + 6y = −8 and 3x − 6y = 36 →
  12. 12.2x + 6y = 8 and 3x + 6y = 6 →
  13. 13.x + y = 5 and x − 2y = −4 →
  14. 14.2x − y = 2 and x + 2y = 11 →
  15. 15.x + 8y = −60 and 8x + y = 24 →
  16. 16.2x + y = 21 and x + y = 15 →
  17. 17.x + 9y = 28 and 9x + y = 12 →
  18. 18.7x + y = 1 and x + 7y = −41 →
  19. 19.x − 3y = −20 and 2x + y = −12 →
  20. 20.x + 5y = 25 and 2x + 6y = 34 →
  21. 21.3x + 3y = −33 and 6x − 2y = 6 →
  22. 22.2x + 4y = 0 and x − 3y = 20 →
  23. 23.4x − 2y = 34 and 6x + 2y = 46 →
  24. 24.6x + 5y = −18 and 2x + 3y = −14 →
  25. 25.x + y = −10 and 3x + 4y = −33 →
  26. 26.3x + 5y = 46 and 5x + 3y = 50 →
  27. 27.6x − y = 5 and 4x + y = 15 →
  28. 28.5x − 5y = −20 and 4x + 5y = −7 →
  29. 29.3x + 4y = 30 and 4x + 3y = 33 →
  30. 30.6x − 5y = −12 and 3x + 3y = 27 →
  31. 31.x + 9y = −61 and 9x + y = −69 →
  32. 32.2x − 6y = 66 and x + y = −3 →
  33. 33.5x + 5y = 15 and x + 6y = 8 →
  34. 34.4x − 2y = 14 and x − y = 0 →
  35. 35.6x − 3y = −15 and 2x + 2y = 16 →
  36. 36.4x + y = 17 and 2x + 2y = 16 →
  37. 37.5x − 4y = 6 and 3x + y = 24 →
  38. 38.6x + 3y = −18 and 3x + 6y = −18 →
  39. 39.6x + 6y = 90 and 2x − 2y = 2 →
  40. 40.x + 2y = 21 and 2x + y = 24 →

Answer key

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

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