Solve for x_1, x_2, x_3
x_{1}=3
x_{2}=-2
x_{3}=1
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x_{1}=-x_{2}-6x_{3}+7
Solve x_{1}+x_{2}+6x_{3}=7 for x_{1}.
-\left(-x_{2}-6x_{3}+7\right)+2x_{2}+9x_{3}=2 -x_{2}-6x_{3}+7-2x_{2}+3x_{3}=10
Substitute -x_{2}-6x_{3}+7 for x_{1} in the second and third equation.
x_{2}=3-5x_{3} x_{3}=-1-x_{2}
Solve these equations for x_{2} and x_{3} respectively.
x_{3}=-1-\left(3-5x_{3}\right)
Substitute 3-5x_{3} for x_{2} in the equation x_{3}=-1-x_{2}.
x_{3}=1
Solve x_{3}=-1-\left(3-5x_{3}\right) for x_{3}.
x_{2}=3-5
Substitute 1 for x_{3} in the equation x_{2}=3-5x_{3}.
x_{2}=-2
Calculate x_{2} from x_{2}=3-5.
x_{1}=-\left(-2\right)-6+7
Substitute -2 for x_{2} and 1 for x_{3} in the equation x_{1}=-x_{2}-6x_{3}+7.
x_{1}=3
Calculate x_{1} from x_{1}=-\left(-2\right)-6+7.
x_{1}=3 x_{2}=-2 x_{3}=1
The system is now solved.
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