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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 26 · 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 = 7 and 3x − 2y = 26 →
  2. 2.x − 3y = −1 and x + y = 11 →
  3. 3.4x + y = −38 and x + 4y = −32 →
  4. 4.3x − 6y = 57 and 2x + y = −7 →
  5. 5.8x + 5y = −89 and 5x + 8y = −80 →
  6. 6.7x + 5y = 69 and 5x + 7y = 63 →
  7. 7.2x + y = −3 and x + 5y = −42 →
  8. 8.4x + 6y = 6 and 4x + 4y = 8 →
  9. 9.3x + 2y = 16 and x + 4y = 2 →
  10. 10.5x + 5y = −60 and 5x + 4y = −53 →
  11. 11.5x + 3y = −13 and 4x + 4y = 4 →
  12. 12.6x + 3y = 57 and 2x + 6y = 24 →
  13. 13.5x + y = −13 and x + 5y = −17 →
  14. 14.9x + y = −75 and x + 9y = 45 →
  15. 15.6x − 5y = −81 and 3x + 3y = 9 →
  16. 16.2x + 6y = −42 and 2x − 6y = 66 →
  17. 17.9x + 8y = 44 and 8x + 9y = 41 →
  18. 18.2x + y = 1 and 2x + 3y = 19 →
  19. 19.3x − y = −26 and 6x + 5y = −59 →
  20. 20.4x − 6y = −38 and x − 4y = −17 →
  21. 21.5x + 6y = 33 and 4x − 2y = −28 →
  22. 22.4x + y = 14 and x + 4y = −19 →
  23. 23.5x + y = −41 and x + 5y = −37 →
  24. 24.3x − 5y = 43 and 2x − 3y = 27 →
  25. 25.4x + 2y = −2 and 2x + 4y = −16 →
  26. 26.2x + 6y = 48 and 6x + 2y = 32 →
  27. 27.2x + 5y = 43 and 6x + 5y = 59 →
  28. 28.5x − 2y = −13 and x + 6y = 23 →
  29. 29.4x + 8y = 64 and 8x + 4y = 44 →
  30. 30.6x − 3y = 39 and 2x − 4y = −2 →
  31. 31.x + 4y = 18 and 4x + y = 27 →
  32. 32.2x + y = 23 and 2x + 6y = 68 →
  33. 33.3x − 2y = −9 and 2x + y = 1 →
  34. 34.3x + 5y = 35 and 4x − 4y = 4 →
  35. 35.6x − y = 9 and 4x − 3y = 13 →
  36. 36.6x + 3y = 21 and 3x + 6y = −12 →
  37. 37.x + 6y = −27 and x − 3y = 18 →
  38. 38.6x − y = 22 and 4x + 2y = 20 →
  39. 39.x + 8y = 20 and 8x + y = 34 →
  40. 40.x + 6y = −31 and 6x + y = 24 →

Answer key

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

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