Matemática discreta Ejemplos

$- 3 y - 3 x = - 9$ , $y = - 3 + 7$

Paso 1

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

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Paso 1.1

Reordena $- 3 y$ y $- 3 x$ .

$- 3 x - 3 y = - 9$

$y = - 3 + 7$

Paso 1.2

Suma $- 3$ y $7$ .

$- 3 x - 3 y = - 9$

$y = 4$

$- 3 x - 3 y = - 9$

$y = 4$

Paso 2

Write the system as a matrix.

$[\begin{array}{c} - 3 & - 3 & - 9 \\ 0 & 1 & 4 \end{array}]$

Paso 3

Obtén la forma escalonada reducida por filas.

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Paso 3.1

Multiply each element of $R_{1}$ by $- \frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

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Paso 3.1.1

Multiply each element of $R_{1}$ by $- \frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{3} \cdot - 3 & - \frac{1}{3} \cdot - 3 & - \frac{1}{3} \cdot - 9 \\ 0 & 1 & 4 \end{array}]$

Paso 3.1.2

Simplifica $R_{1}$ .

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

Paso 3.2

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

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Paso 3.2.1

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

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

Paso 3.2.2

Simplifica $R_{1}$ .

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

Paso 4

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

$x = - 1$

$y = 4$

Paso 5

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

$(- 1, 4)$