\left\{ \begin{array} { l } { x + y = 3 } \\ { y + z = - 6 } \\ { z + x = - 7 } \end{array} \right.
Solve for x, y, z
x=1
y=2
z=-8
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x=-y+3
Solve x+y=3 for x.
z-y+3=-7
Substitute -y+3 for x in the equation z+x=-7.
y=-z-6 z=y-10
Solve the second equation for y and the third equation for z.
z=-z-6-10
Substitute -z-6 for y in the equation z=y-10.
z=-8
Solve z=-z-6-10 for z.
y=-\left(-8\right)-6
Substitute -8 for z in the equation y=-z-6.
y=2
Calculate y from y=-\left(-8\right)-6.
x=-2+3
Substitute 2 for y in the equation x=-y+3.
x=1
Calculate x from x=-2+3.
x=1 y=2 z=-8
The system is now solved.
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