Matemática discreta Exemplos

$- 2 x - 6 y = 8$ , $6 y = - 2 x - 8$

Etapa 1

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

Toque para ver mais passagens...

Etapa 1.1

Some $2 x$ aos dois lados da equação.

$- 2 x - 6 y = 8$

$6 y + 2 x = - 8$

Etapa 1.2

Reordene $6 y$ e $2 x$ .

$- 2 x - 6 y = 8$

$2 x + 6 y = - 8$

$- 2 x - 6 y = 8$

$2 x + 6 y = - 8$

Etapa 2

Write the system as a matrix.

$[\begin{array}{c} - 2 & - 6 & 8 \\ 2 & 6 & - 8 \end{array}]$

Etapa 3

Encontre a forma escalonada reduzida por linhas.

Toque para ver mais passagens...

Etapa 3.1

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

Toque para ver mais passagens...

Etapa 3.1.1

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

$[\begin{array}{c} - \frac{1}{2} \cdot - 2 & - \frac{1}{2} \cdot - 6 & - \frac{1}{2} \cdot 8 \\ 2 & 6 & - 8 \end{array}]$

Etapa 3.1.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & 3 & - 4 \\ 2 & 6 & - 8 \end{array}]$

Etapa 3.2

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

Toque para ver mais passagens...

Etapa 3.2.1

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

$[\begin{array}{c} 1 & 3 & - 4 \\ 2 - 2 \cdot 1 & 6 - 2 \cdot 3 & - 8 - 2 \cdot - 4 \end{array}]$

Etapa 3.2.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & 3 & - 4 \\ 0 & 0 & 0 \end{array}]$

Etapa 4

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

$x + 3 y = - 4$

$0 = 0$

Etapa 5

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

$(- 4 - 3 y, y)$