\left\{ \begin{array} { l } { x _ { 1 } + x _ { 2 } + x _ { 3 } = 3 } \\ { 2 x _ { 1 } - x _ { 2 } + 2 x _ { 3 } = 3 } \\ { 4 x _ { 1 } + x _ { 2 } + x _ { 3 } = 9 } \end{array} \right.
Solve for x_1, x_2, x_3
x_{1}=2
x_{2}=1
x_{3}=0
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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}+2x_{3}=3 4\left(-x_{2}-x_{3}+3\right)+x_{2}+x_{3}=9
Substitute -x_{2}-x_{3}+3 for x_{1} in the second and third equation.
x_{2}=1 x_{3}=-x_{2}+1
Solve these equations for x_{2} and x_{3} respectively.
x_{3}=-1+1
Substitute 1 for x_{2} in the equation x_{3}=-x_{2}+1.
x_{3}=0
Calculate x_{3} from x_{3}=-1+1.
x_{1}=-1-0+3
Substitute 1 for x_{2} and 0 for x_{3} in the equation x_{1}=-x_{2}-x_{3}+3.
x_{1}=2
Calculate x_{1} from x_{1}=-1-0+3.
x_{1}=2 x_{2}=1 x_{3}=0
The system is now solved.
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