Matemática discreta Ejemplos

$4 x - 72 = 72$ , $5 x - 8 y = - 8$

Paso 1

Mueve todos los términos que no contengan una variable al lado derecho de la ecuación.

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Paso 1.1

Suma $72$ a ambos lados de la ecuación.

$4 x = 72 + 72$

$5 x - 8 y = - 8$

Paso 1.2

Suma $72$ y $72$ .

$4 x = 144$

$5 x - 8 y = - 8$

$4 x = 144$

$5 x - 8 y = - 8$

Paso 2

Write the system as a matrix.

$[\begin{array}{c} 4 & 0 & 144 \\ 5 & - 8 & - 8 \end{array}]$

Paso 3

Obtén la forma escalonada reducida por filas.

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Paso 3.1

Multiply each element of $R_{1}$ by $\frac{1}{4}$ to make the entry at $1, 1$ a $1$ .

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Paso 3.1.1

Multiply each element of $R_{1}$ by $\frac{1}{4}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{4}{4} & \frac{0}{4} & \frac{144}{4} \\ 5 & - 8 & - 8 \end{array}]$

Paso 3.1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 36 \\ 5 & - 8 & - 8 \end{array}]$

Paso 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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Paso 3.2.1

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

$[\begin{array}{c} 1 & 0 & 36 \\ 5 - 5 \cdot 1 & - 8 - 5 \cdot 0 & - 8 - 5 \cdot 36 \end{array}]$

Paso 3.2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 36 \\ 0 & - 8 & - 188 \end{array}]$

Paso 3.3

Multiply each element of $R_{2}$ by $- \frac{1}{8}$ to make the entry at $2, 2$ a $1$ .

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Paso 3.3.1

Multiply each element of $R_{2}$ by $- \frac{1}{8}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0 & 36 \\ - \frac{1}{8} \cdot 0 & - \frac{1}{8} \cdot - 8 & - \frac{1}{8} \cdot - 188 \end{array}]$

Paso 3.3.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 36 \\ 0 & 1 & \frac{47}{2} \end{array}]$

Paso 4

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

$x = 36$

$y = \frac{47}{2}$

Paso 5

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

$(36, \frac{47}{2})$