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
|π ππ π|
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.π
simultaneous equations
π1π₯+π1 π¦=π1
π2π₯+π2π¦=π2
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For equating the coefficients of y, let us multiply equation (1) by
and equation (2) by to get,
πππ+πππ=ππ πππ+πππ=ππ
----------- 3
----------- 4
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From equations (5) and (6)
Determinants we get, π = and y =
This method of obtaining solution of simultaneous equations by using determinants
is known as Cramerβs Rule.
Solve the following simultaneous equations using Cramerβs rule.
The given equations are 5 βy = 5π5 + y = 15π
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D = = 5 Γ 1 β (-1 Γ 5) = 5+ 5 = 10
= = 5 Γ 1 β (-1 Γ 15) = 5 + 15 = 20
= =5 Γ 15 β (5 Γ 5) = 75 β 25 = 50
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π = = = 10
y = = = 5
β΄ π = 10 and y = 5 is the solution of the given simultaneous equations.
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