Matemática discreta Ejemplos

$4 x - 5 y = 48$ , $2 x + 3 y = 2$

Paso 1

Write the system as a matrix.

$[\begin{array}{c} 4 & - 5 & 48 \\ 2 & 3 & 2 \end{array}]$

Paso 2

Obtén la forma escalonada reducida por filas.

Toca para ver más pasos...

Paso 2.1

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

Toca para ver más pasos...

Paso 2.1.1

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

$[\begin{array}{c} \frac{4}{4} & \frac{- 5}{4} & \frac{48}{4} \\ 2 & 3 & 2 \end{array}]$

Paso 2.1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{5}{4} & 12 \\ 2 & 3 & 2 \end{array}]$

Paso 2.2

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

Toca para ver más pasos...

Paso 2.2.1

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

$[\begin{array}{c} 1 & - \frac{5}{4} & 12 \\ 2 - 2 \cdot 1 & 3 - 2 (- \frac{5}{4}) & 2 - 2 \cdot 12 \end{array}]$

Paso 2.2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{5}{4} & 12 \\ 0 & \frac{11}{2} & - 22 \end{array}]$

Paso 2.3

Multiply each element of $R_{2}$ by $\frac{2}{11}$ to make the entry at $2, 2$ a $1$ .

Toca para ver más pasos...

Paso 2.3.1

Multiply each element of $R_{2}$ by $\frac{2}{11}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - \frac{5}{4} & 12 \\ \frac{2}{11} \cdot 0 & \frac{2}{11} \cdot \frac{11}{2} & \frac{2}{11} \cdot - 22 \end{array}]$

Paso 2.3.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{5}{4} & 12 \\ 0 & 1 & - 4 \end{array}]$

Paso 2.4

Perform the row operation $R_{1} = R_{1} + \frac{5}{4} R_{2}$ to make the entry at $1, 2$ a $0$ .

Toca para ver más pasos...

Paso 2.4.1

Perform the row operation $R_{1} = R_{1} + \frac{5}{4} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + \frac{5}{4} \cdot 0 & - \frac{5}{4} + \frac{5}{4} \cdot 1 & 12 + \frac{5}{4} \cdot - 4 \\ 0 & 1 & - 4 \end{array}]$

Paso 2.4.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 7 \\ 0 & 1 & - 4 \end{array}]$

Paso 3

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

$x = 7$

$y = - 4$

Paso 4

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

$(7, - 4)$