Matematika Berhingga Contoh

$4 x - 3 y = 5$ , $- 8 x + 6 y = - 10$

Langkah 1

Write the system as a matrix.

$[\begin{array}{c} 4 & - 3 & 5 \\ - 8 & 6 & - 10 \end{array}]$

Langkah 2

Tentukan bentuk eselon baris yang dikurangi.

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Langkah 2.1

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

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Langkah 2.1.1

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

$[\begin{array}{c} \frac{4}{4} & \frac{- 3}{4} & \frac{5}{4} \\ - 8 & 6 & - 10 \end{array}]$

Langkah 2.1.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{3}{4} & \frac{5}{4} \\ - 8 & 6 & - 10 \end{array}]$

Langkah 2.2

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

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Langkah 2.2.1

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

$[\begin{array}{c} 1 & - \frac{3}{4} & \frac{5}{4} \\ - 8 + 8 \cdot 1 & 6 + 8 (- \frac{3}{4}) & - 10 + 8 (\frac{5}{4}) \end{array}]$

Langkah 2.2.2

Sederhanakan $R_{2}$ .

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

Langkah 3

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

$x - \frac{3}{4} y = \frac{5}{4}$

$0 = 0$

Langkah 4

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

$(\frac{5}{4} + \frac{3 y}{4}, y)$