\left\{ \begin{array} { l } { x - 3 y + 3 z = - 1 } \\ { y = - x + 3 } \\ { - 2 x + 3 z = - 4 } \end{array} \right.
Solve for x, y, z
x=2
y=1
z=0
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y=-x+3 x-3y+3z=-1 -2x+3z=-4
Reorder the equations.
y=-x+3
Calculate y from y=-x+3.
x-3\left(-x+3\right)+3z=-1
Substitute -x+3 for y in the equation x-3y+3z=-1.
x=2-\frac{3}{4}z z=-\frac{4}{3}+\frac{2}{3}x
Solve the second equation for x and the third equation for z.
z=-\frac{4}{3}+\frac{2}{3}\left(2-\frac{3}{4}z\right)
Substitute 2-\frac{3}{4}z for x in the equation z=-\frac{4}{3}+\frac{2}{3}x.
z=0
Solve z=-\frac{4}{3}+\frac{2}{3}\left(2-\frac{3}{4}z\right) for z.
x=2-\frac{3}{4}\times 0
Substitute 0 for z in the equation x=2-\frac{3}{4}z.
x=2
Calculate x from x=2-\frac{3}{4}\times 0.
y=-2+3
Substitute 2 for x in the equation y=-x+3.
y=1
Calculate y from y=-2+3.
x=2 y=1 z=0
The system is now solved.
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