simultaneous equations
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Determinant method of solving simultaneous
equations
If a, b, c and d are any four numbers, the value ad-bc is represented
|๐ ๐๐ ๐|
The value of the Determinant is ad-bc.
As it has two rows and two columns It is called as
determinant of order two
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where , , , , and are the real numbers such that
and and y are variables.๐
simultaneous equations
๐1๐ฅ+๐1 ๐ฆ=๐1
๐2๐ฅ+๐2๐ฆ=๐2
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For equating the coefficients of y, let us multiply equation (1) by
and equation (2) by to get,
๐๐๐+๐๐๐=๐๐ ๐๐๐+๐๐๐=๐๐
----------- 3
----------- 4
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From equations (5) and (6)
Determinants we get, ๐ = and y =
This method of obtaining solution of simultaneous equations by using determinants
is known as Cramerโs Rule.
Solve the following simultaneous equations using Cramerโs rule.
The given equations are 5 โy = 5๐5 + y = 15๐
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D = = 5 ร 1 โ (-1 ร 5) = 5+ 5 = 10
= = 5 ร 1 โ (-1 ร 15) = 5 + 15 = 20
= =5 ร 15 โ (5 ร 5) = 75 โ 25 = 50
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๐ = = = 10
y = = = 5
โด ๐ = 10 and y = 5 is the solution of the given simultaneous equations.
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