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Cramer's Rule

In 1750 the German mathematician Gabriel Cramer published a rule for solving a set of n linear equations in n unknowns simultaneously.


Consider a general system of 2 equations in two unknowns

ax + by + c = 0
dx + ey + f = 0

where (ae-db)≠0
Then
x = (bf - ce)/(ae - db) and y = (cd - af)/(ae - db)
This can be written as
with the help of determinants.
Which is an equivalent solution of the simultaneous equations
ax + by = -c
dx + ey = -f
Hence we can denote the solution as the ratio of two determinants D1 and D and D2 and D.

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