\left\{ \begin{array} { l } { x + y = 8 } \\ { y + z = 6 } \\ { z + x = 4 } \end{array} \right.
Solve for x, y, z
x=3
y=5
z=1
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x=-y+8
Solve x+y=8 for x.
z-y+8=4
Substitute -y+8 for x in the equation z+x=4.
y=-z+6 z=y-4
Solve the second equation for y and the third equation for z.
z=-z+6-4
Substitute -z+6 for y in the equation z=y-4.
z=1
Solve z=-z+6-4 for z.
y=-1+6
Substitute 1 for z in the equation y=-z+6.
y=5
Calculate y from y=-1+6.
x=-5+8
Substitute 5 for y in the equation x=-y+8.
x=3
Calculate x from x=-5+8.
x=3 y=5 z=1
The system is now solved.
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