有限数学示例

$[\begin{array}{c} 15 & 8 \\ 4 x & 0 \end{array}] - [\begin{array}{c} 2 & 5 \\ x & 3 y + 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 1

减去相应的元素。

$[\begin{array}{c} 15 - 2 & 8 - 5 \\ 4 x - x & 0 - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 2

Simplify each element.

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解题步骤 2.1

从 $15$ 中减去 $2$ 。

$[\begin{array}{c} 13 & 8 - 5 \\ 4 x - x & 0 - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 2.2

从 $8$ 中减去 $5$ 。

$[\begin{array}{c} 13 & 3 \\ 4 x - x & 0 - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 2.3

从 $4 x$ 中减去 $x$ 。

$[\begin{array}{c} 13 & 3 \\ 3 x & 0 - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 2.4

从 $0$ 中减去 $3 y + 6$ 。

$[\begin{array}{c} 13 & 3 \\ 3 x & - (3 y + 6) \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 2.5

运用分配律。

$[\begin{array}{c} 13 & 3 \\ 3 x & - (3 y) - 1 \cdot 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 2.6

将 $3$ 乘以 $- 1$ 。

$[\begin{array}{c} 13 & 3 \\ 3 x & - 3 y - 1 \cdot 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 2.7

将 $- 1$ 乘以 $6$ 。

$[\begin{array}{c} 13 & 3 \\ 3 x & - 3 y - 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$

解题步骤 3

Write as a linear system of equations.

$13 = 13$

$3 = 3$

$3 x = 12$

$- 3 y - 6 = 4 y + 8$

解题步骤 4

Since $3 = 3$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.

有限数学 示例

有限数学示例