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