\left\{ \begin{array} { l } { x + y + z = 10 } \\ { x + y - z = 20 } \\ { x - y - z = 30 } \end{array} \right.
Solve for x, y, z
x=20
y=-5
z=-5
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x=-y-z+10
Solve x+y+z=10 for x.
-y-z+10+y-z=20 -y-z+10-y-z=30
Substitute -y-z+10 for x in the second and third equation.
z=-5 y=-10-z
Solve these equations for z and y respectively.
y=-10-\left(-5\right)
Substitute -5 for z in the equation y=-10-z.
y=-5
Calculate y from y=-10-\left(-5\right).
x=-\left(-5\right)-\left(-5\right)+10
Substitute -5 for z and -5 for y in the equation x=-y-z+10.
x=20
Calculate x from x=-\left(-5\right)-\left(-5\right)+10.
x=20 y=-5 z=-5
The system is now solved.
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