Solve for x_1, x_2, x_3
x_{1}=4
x_{2}=-2
x_{3}=1
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x_{1}=-x_{2}-x_{3}+3
Solve x_{1}+x_{2}+x_{3}=3 for x_{1}.
2\left(-x_{2}-x_{3}+3\right)-x_{2}+3x_{3}=13 3\left(-x_{2}-x_{3}+3\right)-2x_{2}+x_{3}=17
Substitute -x_{2}-x_{3}+3 for x_{1} in the second and third equation.
x_{2}=-\frac{7}{3}+\frac{1}{3}x_{3} x_{3}=-\frac{5}{2}x_{2}-4
Solve these equations for x_{2} and x_{3} respectively.
x_{3}=-\frac{5}{2}\left(-\frac{7}{3}+\frac{1}{3}x_{3}\right)-4
Substitute -\frac{7}{3}+\frac{1}{3}x_{3} for x_{2} in the equation x_{3}=-\frac{5}{2}x_{2}-4.
x_{3}=1
Solve x_{3}=-\frac{5}{2}\left(-\frac{7}{3}+\frac{1}{3}x_{3}\right)-4 for x_{3}.
x_{2}=-\frac{7}{3}+\frac{1}{3}\times 1
Substitute 1 for x_{3} in the equation x_{2}=-\frac{7}{3}+\frac{1}{3}x_{3}.
x_{2}=-2
Calculate x_{2} from x_{2}=-\frac{7}{3}+\frac{1}{3}\times 1.
x_{1}=-\left(-2\right)-1+3
Substitute -2 for x_{2} and 1 for x_{3} in the equation x_{1}=-x_{2}-x_{3}+3.
x_{1}=4
Calculate x_{1} from x_{1}=-\left(-2\right)-1+3.
x_{1}=4 x_{2}=-2 x_{3}=1
The system is now solved.
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