Matemática discreta Exemplos

$x + y = 9$ , $3 x + 2 y = 22$

Etapa 1

Write the system as a matrix.

$[\begin{array}{c} 1 & 1 & 9 \\ 3 & 2 & 22 \end{array}]$

Etapa 2

Encontre a forma escalonada reduzida por linhas.

Toque para ver mais passagens...

Etapa 2.1

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

Toque para ver mais passagens...

Etapa 2.1.1

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 9 \\ 3 - 3 \cdot 1 & 2 - 3 \cdot 1 & 22 - 3 \cdot 9 \end{array}]$

Etapa 2.1.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 9 \\ 0 & - 1 & - 5 \end{array}]$

Etapa 2.2

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

Toque para ver mais passagens...

Etapa 2.2.1

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

$[\begin{array}{c} 1 & 1 & 9 \\ - 0 & - - 1 & - - 5 \end{array}]$

Etapa 2.2.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 9 \\ 0 & 1 & 5 \end{array}]$

Etapa 2.3

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

Toque para ver mais passagens...

Etapa 2.3.1

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

$[\begin{array}{c} 1 - 0 & 1 - 1 & 9 - 5 \\ 0 & 1 & 5 \end{array}]$

Etapa 2.3.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 4 \\ 0 & 1 & 5 \end{array}]$

Etapa 3

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

$x = 4$

$y = 5$

Etapa 4

The solution is the set of ordered pairs that make the system true.

$(4, 5)$