Date post: | 25-May-2015 |
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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
|𝑎 𝑏𝑐 𝑑|
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.𝓍
simultaneous equations
𝑎1𝑥+𝑏1 𝑦=𝑐1
𝑎2𝑥+𝑏2𝑦=𝑐2
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For equating the coefficients of y, let us multiply equation (1) by
and equation (2) by to get,
𝒂𝟏𝒙+𝒃𝟏𝒚=𝒄𝟏 𝒂𝟐𝒙+𝒃𝟐𝒚=𝒄𝟐
----------- 3
----------- 4
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From equations (5) and (6)
Determinants we get, 𝓍 = and y =
This method of obtaining solution of simultaneous equations by using determinants
is known as Cramer’s Rule.
Solve the following simultaneous equations using Cramer’s rule.
The given equations are 5 –y = 5𝓍5 + y = 15𝓍
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D = = 5 × 1 – (-1 × 5) = 5+ 5 = 10
= = 5 × 1 – (-1 × 15) = 5 + 15 = 20
= =5 × 15 – (5 × 5) = 75 – 25 = 50
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𝓍 = = = 10
y = = = 5
∴ 𝓍 = 10 and y = 5 is the solution of the given simultaneous equations.
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