\left\{ \begin{array} { l } { y = z - x } \\ { 2 x - 3 y + 2 z = 5 } \\ { x + 2 y + z = 13 } \end{array} \right.
Solve for y, z, x
x=2
y=3
z=5
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2x-3\left(z-x\right)+2z=5 x+2\left(z-x\right)+z=13
Substitute z-x for y in the second and third equation.
z=-5+5x x=3z-13
Solve these equations for z and x respectively.
x=3\left(-5+5x\right)-13
Substitute -5+5x for z in the equation x=3z-13.
x=2
Solve x=3\left(-5+5x\right)-13 for x.
z=-5+5\times 2
Substitute 2 for x in the equation z=-5+5x.
z=5
Calculate z from z=-5+5\times 2.
y=5-2
Substitute 5 for z and 2 for x in the equation y=z-x.
y=3
Calculate y from y=5-2.
y=3 z=5 x=2
The system is now solved.
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