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Matemática discreta Exemplos
4x-72y=724x−72y=72 , 5x-8y=-8
Etapa 1
Write the system as a matrix.
[4-72725-8-8]
Etapa 2
Etapa 2.1
Multiply each element of R1 by 14 to make the entry at 1,1 a 1.
Etapa 2.1.1
Multiply each element of R1 by 14 to make the entry at 1,1 a 1.
[44-7247245-8-8]
Etapa 2.1.2
Simplifique R1.
[1-18185-8-8]
[1-18185-8-8]
Etapa 2.2
Perform the row operation R2=R2-5R1 to make the entry at 2,1 a 0.
Etapa 2.2.1
Perform the row operation R2=R2-5R1 to make the entry at 2,1 a 0.
[1-18185-5⋅1-8-5⋅-18-8-5⋅18]
Etapa 2.2.2
Simplifique R2.
[1-1818082-98]
[1-1818082-98]
Etapa 2.3
Multiply each element of R2 by 182 to make the entry at 2,2 a 1.
Etapa 2.3.1
Multiply each element of R2 by 182 to make the entry at 2,2 a 1.
[1-18180828282-9882]
Etapa 2.3.2
Simplifique R2.
[1-181801-4941]
[1-181801-4941]
Etapa 2.4
Perform the row operation R1=R1+18R2 to make the entry at 1,2 a 0.
Etapa 2.4.1
Perform the row operation R1=R1+18R2 to make the entry at 1,2 a 0.
[1+18⋅0-18+18⋅118+18(-4941)01-4941]
Etapa 2.4.2
Simplifique R1.
[10-1444101-4941]
[10-1444101-4941]
[10-1444101-4941]
Etapa 3
Use the result matrix to declare the final solution to the system of equations.
x=-14441
y=-4941
Etapa 4
The solution is the set of ordered pairs that make the system true.
(-14441,-4941)