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