\left\{ \begin{array} { l } { x + 2 y = 2 } \\ { 2 x + 3 y + z = 3 } \\ { 3 x + 4 y + 3 z = 5 } \end{array} \right.
Solve for x, y, z
x=-2
y=2
z=1
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x=2-2y
Solve x+2y=2 for x.
2\left(2-2y\right)+3y+z=3 3\left(2-2y\right)+4y+3z=5
Substitute 2-2y for x in the second and third equation.
y=1+z z=-\frac{1}{3}+\frac{2}{3}y
Solve these equations for y and z respectively.
z=-\frac{1}{3}+\frac{2}{3}\left(1+z\right)
Substitute 1+z for y in the equation z=-\frac{1}{3}+\frac{2}{3}y.
z=1
Solve z=-\frac{1}{3}+\frac{2}{3}\left(1+z\right) for z.
y=1+1
Substitute 1 for z in the equation y=1+z.
y=2
Calculate y from y=1+1.
x=2-2\times 2
Substitute 2 for y in the equation x=2-2y.
x=-2
Calculate x from x=2-2\times 2.
x=-2 y=2 z=1
The system is now solved.
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