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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 848 · 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 + 2y = 2 and 3x − 2y = −12 →
  2. 2.2x + y = 17 and 6x − 6y = 6 →
  3. 3.3x + 8y = 43 and 8x + 3y = 78 →
  4. 4.x + 2y = 20 and x + 3y = 28 →
  5. 5.3x + 4y = −20 and 6x + 3y = 0 →
  6. 6.3x + 6y = 36 and 4x + y = 13 →
  7. 7.4x + 6y = 12 and 6x + 4y = −2 →
  8. 8.6x + 4y = −12 and 5x + 5y = 0 →
  9. 9.7x + 2y = 25 and 2x + 7y = −25 →
  10. 10.9x + 7y = 16 and 7x + 9y = 16 →
  11. 11.2x − 3y = 17 and 3x + 4y = −17 →
  12. 12.2x + 3y = 23 and 3x + 2y = 12 →
  13. 13.x − 2y = 4 and 5x − y = −7 →
  14. 14.2x − 5y = −3 and 6x + 2y = 8 →
  15. 15.x − 5y = −10 and 2x + 3y = 19 →
  16. 16.4x − y = 27 and 3x + 2y = 45 →
  17. 17.8x + 3y = −59 and 3x + 8y = −84 →
  18. 18.6x − y = −59 and 5x − 6y = −75 →
  19. 19.6x + 8y = 40 and 8x + 6y = 16 →
  20. 20.3x + 4y = 3 and 2x + 5y = 9 →
  21. 21.2x − y = −26 and 2x + 5y = 22 →
  22. 22.6x − y = 39 and 6x + 3y = 51 →
  23. 23.4x − y = 21 and 3x + 5y = 56 →
  24. 24.2x + y = −4 and 5x − 6y = 58 →
  25. 25.2x − 2y = 6 and x + 5y = 39 →
  26. 26.5x + 6y = −9 and 3x − 2y = −11 →
  27. 27.5x + y = 0 and 6x + 3y = −9 →
  28. 28.8x + 7y = −50 and 7x + 8y = −55 →
  29. 29.x − 5y = −33 and 6x − 2y = −58 →
  30. 30.5x + 9y = −38 and 9x + 5y = 10 →
  31. 31.x + 3y = −30 and 3x + 6y = −66 →
  32. 32.3x − 6y = −21 and 3x − 5y = −20 →
  33. 33.8x + 4y = 40 and 4x + 8y = 68 →
  34. 34.x + 5y = −27 and 3x + y = 17 →
  35. 35.2x + y = 19 and 3x + 3y = 30 →
  36. 36.6x + 5y = 29 and 3x + y = 13 →
  37. 37.8x + 9y = 93 and 9x + 8y = 94 →
  38. 38.8x + 3y = 30 and 3x + 8y = 25 →
  39. 39.4x + 2y = −14 and 6x − 6y = −48 →
  40. 40.8x + 7y = 120 and 7x + 8y = 120 →

Answer key

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

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