\left\{ \begin{array} { r } { - x + y + z = 3 } \\ { x - y + z = 7 } \\ { x + y - z = 1 } \end{array} \right.
Solve for x, y, z
x=4
y=2
z=5
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x=y+z-3
Solve -x+y+z=3 for x.
y+z-3-y+z=7 y+z-3+y-z=1
Substitute y+z-3 for x in the second and third equation.
z=5 y=2
Solve these equations for z and y respectively.
x=2+5-3
Substitute 5 for z and 2 for y in the equation x=y+z-3.
x=4
Calculate x from x=2+5-3.
x=4 y=2 z=5
The system is now solved.
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