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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 991 · 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. 1.3x − y = −24 and 3x − 5y = −12 →
  2. 2.5x − y = 36 and 3x − 6y = −27 →
  3. 3.4x + 2y = −14 and 3x + y = −11 →
  4. 4.4x + y = −34 and 5x + y = −42 →
  5. 5.4x + 3y = 45 and x − 3y = −15 →
  6. 6.3x + 6y = 42 and 4x − 6y = −56 →
  7. 7.2x + 5y = −14 and 3x − 3y = 21 →
  8. 8.2x + 4y = −16 and 3x + y = 1 →
  9. 9.3x + 4y = 19 and 4x + 3y = 16 →
  10. 10.2x + 4y = −38 and 2x + y = −23 →
  11. 11.6x + 8y = −60 and 8x + 6y = −38 →
  12. 12.7x + 9y = 68 and 9x + 7y = 60 →
  13. 13.3x + 3y = 18 and 2x + 6y = 16 →
  14. 14.2x + 2y = −6 and x + 6y = 17 →
  15. 15.3x + 5y = −12 and 5x + 3y = −36 →
  16. 16.x + 3y = 26 and 3x + y = 30 →
  17. 17.2x + 5y = −21 and 5x − 2y = −38 →
  18. 18.4x + 3y = −1 and 3x + 4y = −6 →
  19. 19.x − y = 0 and 2x + 6y = 48 →
  20. 20.3x − 5y = −55 and 3x − y = −23 →
  21. 21.7x + y = 46 and x + 7y = −14 →
  22. 22.3x + 5y = 69 and 6x − 6y = −6 →
  23. 23.4x + 4y = 0 and 6x − 2y = 48 →
  24. 24.4x + 5y = 29 and 2x + 4y = 16 →
  25. 25.4x + 5y = 17 and 4x + 2y = 14 →
  26. 26.2x − 3y = 6 and 2x + y = 14 →
  27. 27.5x − 3y = 56 and x + 3y = −14 →
  28. 28.3x + 3y = −6 and x + 5y = 26 →
  29. 29.3x + 5y = 63 and 5x + 3y = 57 →
  30. 30.7x + 9y = 79 and 9x + 7y = 65 →
  31. 31.x + 4y = −4 and x + 6y = −10 →
  32. 32.4x + 4y = 48 and x + 6y = 27 →
  33. 33.x + 2y = 6 and x + y = 2 →
  34. 34.7x + 2y = −19 and 2x + 7y = −44 →
  35. 35.7x + 3y = 36 and 3x + 7y = 4 →
  36. 36.2x − 5y = 29 and 5x + 6y = −20 →
  37. 37.x − 4y = −35 and 2x + 2y = 20 →
  38. 38.x + 2y = 9 and 2x + y = −6 →
  39. 39.2x − 4y = 26 and 2x + 5y = −19 →
  40. 40.6x − 3y = −3 and 2x + 6y = 62 →

Answer key

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

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