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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 114 · 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 = 20 and x − 6y = −18 →
  2. 2.2x + 5y = 31 and x + y = 8 →
  3. 3.3x + 4y = −17 and x + y = −3 →
  4. 4.5x + y = −1 and x + 5y = 43 →
  5. 5.3x + y = −25 and 5x + 6y = −33 →
  6. 6.x − y = −13 and 3x + y = −23 →
  7. 7.2x + 2y = 26 and x − 3y = −3 →
  8. 8.6x + 6y = 60 and 6x − y = 18 →
  9. 9.7x + 3y = −25 and 3x + 7y = −45 →
  10. 10.3x + 9y = 102 and 9x + 3y = 90 →
  11. 11.x − 3y = −23 and 4x − 4y = −28 →
  12. 12.5x + 9y = 26 and 9x + 5y = 2 →
  13. 13.6x − 2y = 50 and 3x − 3y = 39 →
  14. 14.3x + 2y = 11 and 2x + 3y = −1 →
  15. 15.5x − y = 8 and 2x − 4y = −22 →
  16. 16.6x − 6y = −18 and 2x + y = 9 →
  17. 17.5x + 6y = 88 and x + 3y = 32 →
  18. 18.5x − 3y = −31 and 2x − 3y = −25 →
  19. 19.6x + 8y = 42 and 8x + 6y = 28 →
  20. 20.5x + 2y = −19 and 2x + 6y = 8 →
  21. 21.3x + 3y = 30 and 2x − 3y = −15 →
  22. 22.5x + 2y = 39 and 2x + 5y = 3 →
  23. 23.5x − 2y = −14 and 2x + 5y = −23 →
  24. 24.2x + 3y = 29 and 2x + 6y = 44 →
  25. 25.5x + 2y = −41 and 6x − y = −39 →
  26. 26.x − 4y = −10 and 3x − 4y = −22 →
  27. 27.2x − 5y = −38 and 5x − y = −3 →
  28. 28.7x + 2y = 11 and 2x + 7y = −29 →
  29. 29.4x − 2y = −36 and 6x + y = −46 →
  30. 30.4x + 2y = 16 and 4x + 5y = 4 →
  31. 31.x + 2y = 15 and 2x + y = 15 →
  32. 32.3x + 2y = 14 and 2x + 3y = 1 →
  33. 33.2x + 8y = 34 and 8x + 2y = 46 →
  34. 34.6x + 7y = −68 and 7x + 6y = −75 →
  35. 35.9x + 3y = 57 and 3x + 9y = 75 →
  36. 36.2x − 4y = −2 and 2x − y = −8 →
  37. 37.x − y = −5 and 2x − y = −2 →
  38. 38.8x + 7y = 52 and 7x + 8y = 53 →
  39. 39.4x + 7y = −46 and 7x + 4y = −31 →
  40. 40.x + y = 3 and 6x − 6y = −6 →

Answer key

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

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