\left\{ \begin{array} { l } { x + y = 5 } \\ { y + z = 6 } \\ { z + x = 9 } \end{array} \right.
Solve for x, y, z
x=4
y=1
z=5
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x=-y+5
Solve x+y=5 for x.
z-y+5=9
Substitute -y+5 for x in the equation z+x=9.
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=5
Solve z=-z+6+4 for z.
y=-5+6
Substitute 5 for z in the equation y=-z+6.
y=1
Calculate y from y=-5+6.
x=-1+5
Substitute 1 for y in the equation x=-y+5.
x=4
Calculate x from x=-1+5.
x=4 y=1 z=5
The system is now solved.
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Limits
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