\left\{ \begin{array} { l } { 2 x + y + 2 = 17 } \\ { x + 2 y + 2 = 14 } \\ { x + y + 2 z = 13 } \end{array} \right.
Solve for x, y, z
x=6
y=3
z=2
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y=-2x+15
Solve 2x+y+2=17 for y.
x+2\left(-2x+15\right)+2=14 x-2x+15+2z=13
Substitute -2x+15 for y in the second and third equation.
x=6 z=\frac{1}{2}x-1
Solve these equations for x and z respectively.
z=\frac{1}{2}\times 6-1
Substitute 6 for x in the equation z=\frac{1}{2}x-1.
z=2
Calculate z from z=\frac{1}{2}\times 6-1.
y=-2\times 6+15
Substitute 6 for x in the equation y=-2x+15.
y=3
Calculate y from y=-2\times 6+15.
x=6 y=3 z=2
The system is now solved.
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