Finite Mathematik Beispiele

$2 x - 5 x = - 3$ , $- 6 x + 15 x = 9$

Schritt 1

Move variables to the left and constant terms to the right.

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Schritt 1.1

Subtrahiere $5 x$ von $2 x$ .

$- 3 x = - 3$

$- 6 x + 15 x = 9$

Schritt 1.2

Addiere $- 6 x$ und $15 x$ .

$- 3 x = - 3$

$9 x = 9$

$- 3 x = - 3$

$9 x = 9$

Schritt 2

Write the system as a matrix.

$[\begin{array}{c} - 3 & - 3 \\ 9 & 9 \end{array}]$

Schritt 3

Ermittele die normierte Zeilenstufenform.

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Schritt 3.1

Multiply each element of $R_{1}$ by $- \frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

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Schritt 3.1.1

Multiply each element of $R_{1}$ by $- \frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{3} \cdot - 3 & - \frac{1}{3} \cdot - 3 \\ 9 & 9 \end{array}]$

Schritt 3.1.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 1 \\ 9 & 9 \end{array}]$

Schritt 3.2

Perform the row operation $R_{2} = R_{2} - 9 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Schritt 3.2.1

Perform the row operation $R_{2} = R_{2} - 9 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 \\ 9 - 9 \cdot 1 & 9 - 9 \cdot 1 \end{array}]$

Schritt 3.2.2

Vereinfache $R_{2}$ .

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

Schritt 4

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

$x = 1$

$0 = 0$

Schritt 5

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

$(error = error)$