Solve for x_1, x_2, x_3
x_{1}=-1
x_{2}=2
x_{3}=1
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x_{2}=-2x_{1}-x_{3}+1
Solve 2x_{1}+x_{2}+x_{3}=1 for x_{2}.
2x_{1}-2\left(-2x_{1}-x_{3}+1\right)-x_{3}=-7 4x_{1}-2x_{1}-x_{3}+1+3x_{3}=1
Substitute -2x_{1}-x_{3}+1 for x_{2} in the second and third equation.
x_{1}=-\frac{1}{6}x_{3}-\frac{5}{6} x_{3}=-x_{1}
Solve these equations for x_{1} and x_{3} respectively.
x_{3}=-\left(-\frac{1}{6}x_{3}-\frac{5}{6}\right)
Substitute -\frac{1}{6}x_{3}-\frac{5}{6} for x_{1} in the equation x_{3}=-x_{1}.
x_{3}=1
Solve x_{3}=-\left(-\frac{1}{6}x_{3}-\frac{5}{6}\right) for x_{3}.
x_{1}=-\frac{1}{6}-\frac{5}{6}
Substitute 1 for x_{3} in the equation x_{1}=-\frac{1}{6}x_{3}-\frac{5}{6}.
x_{1}=-1
Calculate x_{1} from x_{1}=-\frac{1}{6}-\frac{5}{6}.
x_{2}=-2\left(-1\right)-1+1
Substitute -1 for x_{1} and 1 for x_{3} in the equation x_{2}=-2x_{1}-x_{3}+1.
x_{2}=2
Calculate x_{2} from x_{2}=-2\left(-1\right)-1+1.
x_{1}=-1 x_{2}=2 x_{3}=1
The system is now solved.
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