$\"\"$

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The system of linear equations are

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$\"\"$ (Equation 1)

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$\"\"$ (Equation 2)

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$\"\"$ (Equation 3)

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In this system leading of coefficient of the first equation does not one, so the system of linear equations rewrite as follows:

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$\"\"$ (Equation 1)

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$\"\"$ (Equation 2)

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$\"\"$ (Equation 3)

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The leading of coefficient of the first equation is one, you can begin by saving the y at the upper left and eliminating the other y - terms from the first column.So, adding negative three times the first equation to the third equation produces a new third equation.

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$\"\"$ $\"\"$

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So, the new system of equations are

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$\"\"$ (Equation 1)

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$\"\"$ (Equation 2)

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$\"\"$ (Equation 3)

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Adding negative two times the second equation to the third equation produces a new third equation.

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$\"\"$ $\"\"$

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So, the new system of equations are

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$\"\"$ (Equation 1)

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$\"\"$ (Equation 2)

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$\"\"$ (Equation 3)

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The statement $\"\"$ is true, you can conclude that this system will have infinitely many solutions.

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In the above system, multiply the equation 2 and next equation 1 and 2 are interchange as follows:

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$\"\"$ (Equation 1)

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$\"\"$ (Equation 2) $\"\"$

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In the second equation, solve for x in terms of z to obtain $\"\"$ .

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By back - substituting $\"\"$ into equation 1, you can solve for y, as follows:

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$\"\"$ (Write equation 1)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify)

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$\"\"$ (Subtract $\"\"$ from each side)

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Finally let $\"\"$ , where a is a real number, the solutions of the system

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$\"\"$ . $\"\"$

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The solution in ordered triple form is $\"\"$ .