Matematika Berhingga Contoh

$8 x - 7 y = - 5$ , $- 16 x + 14 y = 10$

Langkah 1

Write the system as a matrix.

$[\begin{array}{c} 8 & - 7 & - 5 \\ - 16 & 14 & 10 \end{array}]$

Langkah 2

Tentukan bentuk eselon baris yang dikurangi.

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Langkah 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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Langkah 2.1.1

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

$[\begin{array}{c} \frac{8}{8} & \frac{- 7}{8} & \frac{- 5}{8} \\ - 16 & 14 & 10 \end{array}]$

Langkah 2.1.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & - \frac{5}{8} \\ - 16 & 14 & 10 \end{array}]$

Langkah 2.2

Perform the row operation $R_{2} = R_{2} + 16 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Langkah 2.2.1

Perform the row operation $R_{2} = R_{2} + 16 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & - \frac{5}{8} \\ - 16 + 16 \cdot 1 & 14 + 16 (- \frac{7}{8}) & 10 + 16 (- \frac{5}{8}) \end{array}]$

Langkah 2.2.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & - \frac{5}{8} \\ 0 & 0 & 0 \end{array}]$

Langkah 3

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

$x - \frac{7}{8} y = - \frac{5}{8}$

$0 = 0$

Langkah 4

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

$(- \frac{5}{8} + \frac{7 y}{8}, y)$