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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 148 · 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. 1.9x + y = −3 and x + 9y = 53 →
  2. 2.5x + 2y = 36 and 2x + 5y = 6 →
  3. 3.x + 8y = 34 and 8x + y = 20 →
  4. 4.3x + 5y = 34 and 5x − 2y = 36 →
  5. 5.x + 5y = −43 and 5x + y = −23 →
  6. 6.5x + 2y = 29 and 6x + 5y = 53 →
  7. 7.x + 4y = −12 and 4x + y = −18 →
  8. 8.8x + 3y = 29 and 3x + 8y = 59 →
  9. 9.3x + 5y = 16 and 5x + 3y = 16 →
  10. 10.x + y = 1 and 6x − 4y = −84 →
  11. 11.9x + 2y = 80 and 2x + 9y = 52 →
  12. 12.2x − y = −12 and 6x − y = −40 →
  13. 13.6x + y = 9 and x + 6y = −51 →
  14. 14.2x + y = 8 and x + 2y = 7 →
  15. 15.3x + 2y = 20 and 6x − 3y = −9 →
  16. 16.5x + 8y = −6 and 8x + 5y = −33 →
  17. 17.x − 3y = 29 and 6x + 6y = −42 →
  18. 18.x + 5y = −50 and 2x + 3y = −37 →
  19. 19.2x + 6y = −48 and 6x + 2y = 0 →
  20. 20.7x + 6y = 76 and 6x + 7y = 80 →
  21. 21.5x − 4y = −15 and 4x − y = −23 →
  22. 22.3x + 7y = 29 and 7x + 3y = −39 →
  23. 23.4x − 2y = 54 and 4x + 2y = 18 →
  24. 24.4x + y = −11 and 3x + 3y = −6 →
  25. 25.3x + 6y = 72 and 3x − 4y = −8 →
  26. 26.4x + 3y = −17 and 3x + 4y = −11 →
  27. 27.8x + 2y = 38 and 2x + 8y = 32 →
  28. 28.9x + 7y = 13 and 7x + 9y = 35 →
  29. 29.9x + 3y = 42 and 3x + 9y = 54 →
  30. 30.3x + 2y = 9 and x − 3y = 25 →
  31. 31.5x − 5y = 65 and 5x + 2y = 16 →
  32. 32.7x + 6y = −17 and 6x + 7y = −9 →
  33. 33.2x − y = −23 and 5x + 5y = 10 →
  34. 34.4x + 2y = 6 and 2x + 4y = 6 →
  35. 35.6x + 5y = 34 and 2x + 2y = 10 →
  36. 36.5x + 5y = 65 and 5x − 6y = 21 →
  37. 37.6x + 5y = −18 and 5x + 4y = −16 →
  38. 38.2x + 5y = −11 and 5x + 6y = −34 →
  39. 39.2x − 4y = −14 and x + 3y = −12 →
  40. 40.3x + 2y = −22 and 4x + y = −26 →

Answer key

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

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