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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 265 · 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.x − y = 13 and 4x + y = 7 →
  2. 2.6x + y = 40 and x + 6y = 30 →
  3. 3.5x + y = −21 and 6x + 3y = −18 →
  4. 4.7x + 5y = −108 and 5x + 7y = −108 →
  5. 5.4x + 2y = −8 and 5x − 4y = 42 →
  6. 6.6x + y = 46 and 2x + y = 14 →
  7. 7.2x + 6y = −6 and 6x + 2y = 46 →
  8. 8.3x + y = 10 and 3x − 5y = −14 →
  9. 9.6x + 2y = −10 and 2x + 6y = 2 →
  10. 10.6x + 2y = 6 and 2x + 6y = −46 →
  11. 11.3x − 3y = 9 and 6x + 6y = 30 →
  12. 12.x + 2y = −1 and 6x − 2y = 22 →
  13. 13.5x − y = 47 and 6x + y = 41 →
  14. 14.x + 7y = 45 and 7x + y = −21 →
  15. 15.5x + 3y = −48 and 3x + 5y = −32 →
  16. 16.3x + 7y = 41 and 7x + 3y = −11 →
  17. 17.3x − 4y = 2 and 4x − 2y = −4 →
  18. 18.2x − 6y = −32 and 5x + y = 32 →
  19. 19.x + 5y = 43 and 2x − 4y = −12 →
  20. 20.2x − 4y = 18 and x + 5y = −12 →
  21. 21.2x + 6y = 58 and 2x − 2y = −14 →
  22. 22.2x − 5y = 27 and 5x + y = 27 →
  23. 23.3x + 5y = 36 and 2x + 2y = 16 →
  24. 24.3x + 4y = 34 and 6x − 3y = 24 →
  25. 25.5x + 5y = −15 and x + 2y = −1 →
  26. 26.x + 7y = −17 and 7x + y = −23 →
  27. 27.3x + y = 16 and x + 3y = 16 →
  28. 28.2x + 4y = 42 and 4x + 2y = 48 →
  29. 29.3x − 2y = −16 and 4x − y = −13 →
  30. 30.3x + y = −16 and 3x + 2y = −14 →
  31. 31.3x + 4y = 2 and 2x − 4y = 28 →
  32. 32.x + 3y = −1 and 4x + 5y = −18 →
  33. 33.3x + 4y = 23 and 3x + 3y = 24 →
  34. 34.2x + 4y = 10 and 4x + 2y = −4 →
  35. 35.x − 3y = −15 and x + y = −3 →
  36. 36.6x + 9y = 0 and 9x + 6y = 45 →
  37. 37.3x − y = 13 and 4x + y = 15 →
  38. 38.2x + 6y = 42 and 5x + 5y = 65 →
  39. 39.6x + y = −37 and x + 6y = 23 →
  40. 40.5x + 3y = −19 and 6x + y = −41 →

Answer key

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

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