Solve for x_1, x_2, x_3
x_{1}=1
x_{2}=2
x_{3}=3
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x_{1}=-2x_{2}-x_{3}+8
Solve x_{1}+2x_{2}+x_{3}=8 for x_{1}.
3\left(-2x_{2}-x_{3}+8\right)+2x_{2}+x_{3}=10 4\left(-2x_{2}-x_{3}+8\right)+3x_{2}-2x_{3}=4
Substitute -2x_{2}-x_{3}+8 for x_{1} in the second and third equation.
x_{2}=\frac{7}{2}-\frac{1}{2}x_{3} x_{3}=-\frac{5}{6}x_{2}+\frac{14}{3}
Solve these equations for x_{2} and x_{3} respectively.
x_{3}=-\frac{5}{6}\left(\frac{7}{2}-\frac{1}{2}x_{3}\right)+\frac{14}{3}
Substitute \frac{7}{2}-\frac{1}{2}x_{3} for x_{2} in the equation x_{3}=-\frac{5}{6}x_{2}+\frac{14}{3}.
x_{3}=3
Solve x_{3}=-\frac{5}{6}\left(\frac{7}{2}-\frac{1}{2}x_{3}\right)+\frac{14}{3} for x_{3}.
x_{2}=\frac{7}{2}-\frac{1}{2}\times 3
Substitute 3 for x_{3} in the equation x_{2}=\frac{7}{2}-\frac{1}{2}x_{3}.
x_{2}=2
Calculate x_{2} from x_{2}=\frac{7}{2}-\frac{1}{2}\times 3.
x_{1}=-2\times 2-3+8
Substitute 2 for x_{2} and 3 for x_{3} in the equation x_{1}=-2x_{2}-x_{3}+8.
x_{1}=1
Calculate x_{1} from x_{1}=-2\times 2-3+8.
x_{1}=1 x_{2}=2 x_{3}=3
The system is now solved.
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