\left\{ \begin{array} { l } { x + y = 2 } \\ { x + z + y = 10 } \\ { z - y = 5 } \end{array} \right.
Solve for x, y, z
x=-1
y=3
z=8
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x=-y+2
Solve x+y=2 for x.
-y+2+z+y=10
Substitute -y+2 for x in the equation x+z+y=10.
z=8 y=z-5
Solve the second equation for z and the third equation for y.
y=8-5
Substitute 8 for z in the equation y=z-5.
y=3
Calculate y from y=8-5.
x=-3+2
Substitute 3 for y in the equation x=-y+2.
x=-1
Calculate x from x=-3+2.
x=-1 y=3 z=8
The system is now solved.
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