\left\{ \begin{array} { l } { 1 \cdot x + y - z = 1 } \\ { 0 \cdot x - y + z = - 1 } \\ { - x - y + 2 z = 3 } \end{array} \right.
Solve for x, y, z
x=0
y=5
z=4
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y=-x+z+1
Solve 1x+y-z=1 for y.
0x-\left(-x+z+1\right)+z=-1 -x-\left(-x+z+1\right)+2z=3
Substitute -x+z+1 for y in the second and third equation.
x=0 z=4
Solve these equations for x and z respectively.
y=-0+4+1
Substitute 0 for x and 4 for z in the equation y=-x+z+1.
y=5
Calculate y from y=-0+4+1.
x=0 y=5 z=4
The system is now solved.
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