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$- 10 x - 3 y = - 41$ , $4 x + y = 17$

Bước 1

Write the system as a matrix.

$[\begin{array}{c} - 10 & - 3 & - 41 \\ 4 & 1 & 17 \end{array}]$

Bước 2

Tìm dạng ma trận hàng bậc thang rút gọn.

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Bước 2.1

Multiply each element of $R_{1}$ by $- \frac{1}{10}$ to make the entry at $1, 1$ a $1$ .

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Bước 2.1.1

Multiply each element of $R_{1}$ by $- \frac{1}{10}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{10} \cdot - 10 & - \frac{1}{10} \cdot - 3 & - \frac{1}{10} \cdot - 41 \\ 4 & 1 & 17 \end{array}]$

Bước 2.1.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & \frac{3}{10} & \frac{41}{10} \\ 4 & 1 & 17 \end{array}]$

Bước 2.2

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Bước 2.2.1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{3}{10} & \frac{41}{10} \\ 4 - 4 \cdot 1 & 1 - 4 (\frac{3}{10}) & 17 - 4 (\frac{41}{10}) \end{array}]$

Bước 2.2.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & \frac{3}{10} & \frac{41}{10} \\ 0 & - \frac{1}{5} & \frac{3}{5} \end{array}]$

Bước 2.3

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

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Bước 2.3.1

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

$[\begin{array}{c} 1 & \frac{3}{10} & \frac{41}{10} \\ - 5 \cdot 0 & - 5 (- \frac{1}{5}) & - 5 (\frac{3}{5}) \end{array}]$

Bước 2.3.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & \frac{3}{10} & \frac{41}{10} \\ 0 & 1 & - 3 \end{array}]$

Bước 2.4

Perform the row operation $R_{1} = R_{1} - \frac{3}{10} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Bước 2.4.1

Perform the row operation $R_{1} = R_{1} - \frac{3}{10} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{3}{10} \cdot 0 & \frac{3}{10} - \frac{3}{10} \cdot 1 & \frac{41}{10} - \frac{3}{10} \cdot - 3 \\ 0 & 1 & - 3 \end{array}]$

Bước 2.4.2

Rút gọn $R_{1}$ .

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

Bước 3

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

$x = 5$

$y = - 3$

Bước 4

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

$(5, - 3)$