有限数学 示例

Solve Using a Matrix by Elimination 1800=6x+2y+z , 1400=4x+4y+2z , 700=3x+3y+3z
, ,
解题步骤 1
Move variables to the left and constant terms to the right.
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解题步骤 1.1
将所有包含变量的项移到等式左边。
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解题步骤 1.1.1
从等式两边同时减去
解题步骤 1.1.2
从等式两边同时减去
解题步骤 1.1.3
从等式两边同时减去
解题步骤 1.2
从等式两边同时减去
解题步骤 1.3
将所有包含变量的项移到等式左边。
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解题步骤 1.3.1
从等式两边同时减去
解题步骤 1.3.2
从等式两边同时减去
解题步骤 1.3.3
从等式两边同时减去
解题步骤 1.4
从等式两边同时减去
解题步骤 1.5
将所有包含变量的项移到等式左边。
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解题步骤 1.5.1
从等式两边同时减去
解题步骤 1.5.2
从等式两边同时减去
解题步骤 1.5.3
从等式两边同时减去
解题步骤 1.6
从等式两边同时减去
解题步骤 2
Write the system as a matrix.
解题步骤 3
求行简化阶梯形矩阵。
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解题步骤 3.1
Multiply each element of by to make the entry at a .
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解题步骤 3.1.1
Multiply each element of by to make the entry at a .
解题步骤 3.1.2
化简
解题步骤 3.2
Perform the row operation to make the entry at a .
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解题步骤 3.2.1
Perform the row operation to make the entry at a .
解题步骤 3.2.2
化简
解题步骤 3.3
Perform the row operation to make the entry at a .
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解题步骤 3.3.1
Perform the row operation to make the entry at a .
解题步骤 3.3.2
化简
解题步骤 3.4
Multiply each element of by to make the entry at a .
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解题步骤 3.4.1
Multiply each element of by to make the entry at a .
解题步骤 3.4.2
化简
解题步骤 3.5
Perform the row operation to make the entry at a .
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解题步骤 3.5.1
Perform the row operation to make the entry at a .
解题步骤 3.5.2
化简
解题步骤 3.6
Multiply each element of by to make the entry at a .
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解题步骤 3.6.1
Multiply each element of by to make the entry at a .
解题步骤 3.6.2
化简
解题步骤 3.7
Perform the row operation to make the entry at a .
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解题步骤 3.7.1
Perform the row operation to make the entry at a .
解题步骤 3.7.2
化简
解题步骤 3.8
Perform the row operation to make the entry at a .
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解题步骤 3.8.1
Perform the row operation to make the entry at a .
解题步骤 3.8.2
化简
解题步骤 3.9
Perform the row operation to make the entry at a .
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解题步骤 3.9.1
Perform the row operation to make the entry at a .
解题步骤 3.9.2
化简
解题步骤 4
Use the result matrix to declare the final solution to the system of equations.
解题步骤 5
The solution is the set of ordered pairs that make the system true.