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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 210 · 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. 1.5x + 2y = 57 and 2x + 5y = 48 →
  2. 2.2x + 3y = −36 and 3x + 2y = −39 →
  3. 3.5x + y = 38 and x + y = 14 →
  4. 4.5x + y = −3 and 3x − 4y = 35 →
  5. 5.5x − 6y = −13 and 5x − 4y = −17 →
  6. 6.x + 6y = −4 and x + y = 1 →
  7. 7.5x + 3y = −38 and 3x + 5y = −26 →
  8. 8.x + 3y = 6 and 4x − 6y = 42 →
  9. 9.3x − 2y = 30 and 6x − 5y = 66 →
  10. 10.4x + y = 15 and 5x + 6y = 33 →
  11. 11.9x + 2y = −55 and 2x + 9y = 22 →
  12. 12.x − 4y = 28 and 3x + 2y = 14 →
  13. 13.6x + 2y = 26 and x + 5y = 23 →
  14. 14.6x + y = 32 and 6x − y = 16 →
  15. 15.6x + 2y = 14 and 2x + 5y = 9 →
  16. 16.7x + 4y = 25 and 4x + 7y = 19 →
  17. 17.3x − y = 3 and 4x + 2y = −26 →
  18. 18.3x − y = −7 and 4x + y = −7 →
  19. 19.x − y = 2 and 4x + 5y = 17 →
  20. 20.8x + 2y = 6 and 2x + 8y = −6 →
  21. 21.6x + 3y = −78 and 3x + 6y = −75 →
  22. 22.2x − y = −8 and 6x + y = −8 →
  23. 23.x + y = 9 and 6x + 2y = 42 →
  24. 24.7x + 2y = 32 and 2x + 7y = 22 →
  25. 25.5x − 5y = −5 and 4x + 3y = 24 →
  26. 26.2x + y = 5 and x − 2y = 5 →
  27. 27.9x + 7y = 88 and 7x + 9y = 72 →
  28. 28.x + 2y = 8 and 2x + y = −5 →
  29. 29.x + 3y = 35 and 3x + y = 33 →
  30. 30.6x + 4y = 8 and 6x + 5y = 4 →
  31. 31.5x + 5y = 25 and 3x + 6y = 24 →
  32. 32.8x + 6y = 50 and 6x + 8y = 48 →
  33. 33.2x + 8y = 8 and 8x + 2y = −28 →
  34. 34.2x + 4y = −22 and 3x + 3y = −15 →
  35. 35.4x + 5y = −11 and 4x − 4y = 16 →
  36. 36.x + 3y = −3 and 6x − 3y = −39 →
  37. 37.5x + 7y = −37 and 7x + 5y = −47 →
  38. 38.3x − 6y = 18 and 5x − 6y = 10 →
  39. 39.x + 2y = −23 and 2x + 2y = −28 →
  40. 40.x + y = 2 and 2x + 6y = 20 →

Answer key

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

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