Matemática discreta Exemplos

Resolva Usando uma Matriz por Eliminação 30x+25y=430 , 2x+0.4y=16
30x+25y=430 , 2x+0.4y=16
Etapa 1
Write the system as a matrix.
[302543020.416]
Etapa 2
Encontre a forma escalonada reduzida por linhas.
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Etapa 2.1
Multiply each element of R1 by 130 to make the entry at 1,1 a 1.
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Etapa 2.1.1
Multiply each element of R1 by 130 to make the entry at 1,1 a 1.
[303025304303020.416]
Etapa 2.1.2
Simplifique R1.
[15643320.416]
[15643320.416]
Etapa 2.2
Perform the row operation R2=R2-2R1 to make the entry at 2,1 a 0.
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Etapa 2.2.1
Perform the row operation R2=R2-2R1 to make the entry at 2,1 a 0.
[1564332-210.4-2(56)16-2(433)]
Etapa 2.2.2
Simplifique R2.
[1564330-1.26-383]
[1564330-1.26-383]
Etapa 2.3
Multiply each element of R2 by 1-1.26 to make the entry at 2,2 a 1.
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Etapa 2.3.1
Multiply each element of R2 by 1-1.26 to make the entry at 2,2 a 1.
[1564330-1.26-1.26-1.26-383-1.26]
Etapa 2.3.2
Simplifique R2.
[1564330110]
[1564330110]
Etapa 2.4
Perform the row operation R1=R1-56R2 to make the entry at 1,2 a 0.
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Etapa 2.4.1
Perform the row operation R1=R1-56R2 to make the entry at 1,2 a 0.
[1-56056-561433-56100110]
Etapa 2.4.2
Simplifique R1.
[1060110]
[1060110]
[1060110]
Etapa 3
Use the result matrix to declare the final solution to the system of equations.
x=6
y=10
Etapa 4
The solution is the set of ordered pairs that make the system true.
(6,10)
30x+25y=430,2x+0.4y=16
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