Precalcolo Esempi

$- 8 x - 3 y = - 8$ , $- 6 x - y = - 4$

Passaggio 1

Write the system as a matrix.

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

Passaggio 2

Trova la forma ridotta a scala per righe di Echelon.

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Passaggio 2.1

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

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Passaggio 2.1.1

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

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

Passaggio 2.1.2

Semplifica $R_{1}$ .

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

Passaggio 2.2

Perform the row operation $R_{2} = R_{2} + 6 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Passaggio 2.2.1

Perform the row operation $R_{2} = R_{2} + 6 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{3}{8} & 1 \\ - 6 + 6 \cdot 1 & - 1 + 6 (\frac{3}{8}) & - 4 + 6 \cdot 1 \end{array}]$

Passaggio 2.2.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & \frac{3}{8} & 1 \\ 0 & \frac{5}{4} & 2 \end{array}]$

Passaggio 2.3

Multiply each element of $R_{2}$ by $\frac{4}{5}$ to make the entry at $2, 2$ a $1$ .

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Passaggio 2.3.1

Multiply each element of $R_{2}$ by $\frac{4}{5}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{3}{8} & 1 \\ \frac{4}{5} \cdot 0 & \frac{4}{5} \cdot \frac{5}{4} & \frac{4}{5} \cdot 2 \end{array}]$

Passaggio 2.3.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & \frac{3}{8} & 1 \\ 0 & 1 & \frac{8}{5} \end{array}]$

Passaggio 2.4

Perform the row operation $R_{1} = R_{1} - \frac{3}{8} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Passaggio 2.4.1

Perform the row operation $R_{1} = R_{1} - \frac{3}{8} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{3}{8} \cdot 0 & \frac{3}{8} - \frac{3}{8} \cdot 1 & 1 - \frac{3}{8} \cdot \frac{8}{5} \\ 0 & 1 & \frac{8}{5} \end{array}]$

Passaggio 2.4.2

Semplifica $R_{1}$ .

$[\begin{array}{c} 1 & 0 & \frac{2}{5} \\ 0 & 1 & \frac{8}{5} \end{array}]$

Passaggio 3

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

$x = \frac{2}{5}$

$y = \frac{8}{5}$

Passaggio 4

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

$(\frac{2}{5}, \frac{8}{5})$