Matemática discreta Exemplos

$5 x \cdot 1 - 3 x \cdot 2 = 20$ , $7 x \cdot 1 - 6 x \cdot 2 = 10$

Etapa 1

Move variables to the left and constant terms to the right.

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Etapa 1.1

Simplifique cada termo.

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Etapa 1.1.1

Multiplique $5$ por $1$ .

$5 x - 3 x \cdot 2 = 20$

$7 x \cdot 1 - 6 x \cdot 2 = 10$

Etapa 1.1.2

Multiplique $2$ por $- 3$ .

$5 x - 6 x = 20$

$7 x \cdot 1 - 6 x \cdot 2 = 10$

$5 x - 6 x = 20$

$7 x \cdot 1 - 6 x \cdot 2 = 10$

Etapa 1.2

Subtraia $6 x$ de $5 x$ .

$- x = 20$

$7 x \cdot 1 - 6 x \cdot 2 = 10$

Etapa 1.3

Simplifique cada termo.

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Etapa 1.3.1

Multiplique $7$ por $1$ .

$- x = 20$

$7 x - 6 x \cdot 2 = 10$

Etapa 1.3.2

Multiplique $2$ por $- 6$ .

$- x = 20$

$7 x - 12 x = 10$

$- x = 20$

$7 x - 12 x = 10$

Etapa 1.4

Subtraia $12 x$ de $7 x$ .

$- x = 20$

$- 5 x = 10$

$- x = 20$

$- 5 x = 10$

Etapa 2

Write the system as a matrix.

$[\begin{array}{c} - 1 & 20 \\ - 5 & 10 \end{array}]$

Etapa 3

Encontre a forma escalonada reduzida por linhas.

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Etapa 3.1

Multiply each element of $R_{1}$ by $- 1$ to make the entry at $1, 1$ a $1$ .

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Etapa 3.1.1

Multiply each element of $R_{1}$ by $- 1$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - - 1 & - 1 \cdot 20 \\ - 5 & 10 \end{array}]$

Etapa 3.1.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & - 20 \\ - 5 & 10 \end{array}]$

Etapa 3.2

Perform the row operation $R_{2} = R_{2} + 5 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Etapa 3.2.1

Perform the row operation $R_{2} = R_{2} + 5 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - 20 \\ - 5 + 5 \cdot 1 & 10 + 5 \cdot - 20 \end{array}]$

Etapa 3.2.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & - 20 \\ 0 & - 90 \end{array}]$

Etapa 3.3

Multiply each element of $R_{2}$ by $- \frac{1}{90}$ to make the entry at $2, 2$ a $1$ .

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Etapa 3.3.1

Multiply each element of $R_{2}$ by $- \frac{1}{90}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - 20 \\ - \frac{1}{90} \cdot 0 & - \frac{1}{90} \cdot - 90 \end{array}]$

Etapa 3.3.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & - 20 \\ 0 & 1 \end{array}]$

Etapa 3.4

Perform the row operation $R_{1} = R_{1} + 20 R_{2}$ to make the entry at $1, 2$ a $0$ .

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Etapa 3.4.1

Perform the row operation $R_{1} = R_{1} + 20 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + 20 \cdot 0 & - 20 + 20 \cdot 1 \\ 0 & 1 \end{array}]$

Etapa 3.4.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Etapa 4

Use the result matrix to declare the final solution to the system of equations.

$x = 0$

$0 = 1$

Etapa 5

The system is inconsistent so there is no solution.

$Nenhuma solução$