Matematica discreta Esempi

$x + 5 y = 10$ , $3 x + 15 y = 30$

Passaggio 1

Write the system as a matrix.

$[\begin{array}{c} 1 & 5 & 10 \\ 3 & 15 & 30 \end{array}]$

Passaggio 2

Trova la forma ridotta a scala per righe di Echelon.

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Passaggio 2.1

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

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Passaggio 2.1.1

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

$[\begin{array}{c} 1 & 5 & 10 \\ 3 - 3 \cdot 1 & 15 - 3 \cdot 5 & 30 - 3 \cdot 10 \end{array}]$

Passaggio 2.1.2

Semplifica $R_{2}$ .

$[\begin{array}{c} 1 & 5 & 10 \\ 0 & 0 & 0 \end{array}]$

Passaggio 3

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

$x + 5 y = 10$

$0 = 0$

Passaggio 4

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

$(10 - 5 y, y)$