初级微积分示例

$x - 8 = 8$ , $4 x + 3 y = 2$

解题步骤 1

将所有不包含变量的项移到等式右边。

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解题步骤 1.1

在等式两边都加上 $8$ 。

$x = 8 + 8$

$4 x + 3 y = 2$

解题步骤 1.2

将 $8$ 和 $8$ 相加。

$x = 16$

$4 x + 3 y = 2$

$x = 16$

$4 x + 3 y = 2$

解题步骤 2

Write the system as a matrix.

$[\begin{array}{c} 1 & 0 & 16 \\ 4 & 3 & 2 \end{array}]$

解题步骤 3

求行简化阶梯形矩阵。

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解题步骤 3.1

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

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解题步骤 3.1.1

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

$[\begin{array}{c} 1 & 0 & 16 \\ 4 - 4 \cdot 1 & 3 - 4 \cdot 0 & 2 - 4 \cdot 16 \end{array}]$

解题步骤 3.1.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 0 & 16 \\ 0 & 3 & - 62 \end{array}]$

解题步骤 3.2

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

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解题步骤 3.2.1

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0 & 16 \\ \frac{0}{3} & \frac{3}{3} & \frac{- 62}{3} \end{array}]$

解题步骤 3.2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 0 & 16 \\ 0 & 1 & - \frac{62}{3} \end{array}]$

解题步骤 4

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

$x = 16$

$y = - \frac{62}{3}$

解题步骤 5

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

$(16, - \frac{62}{3})$

初级微积分 示例