\left\{ \begin{array} { l } { x + y + z = 2 } \\ { 2 x - 3 y = 5 } \\ { y + z = 1 } \end{array} \right.
Solve for x, y, z
x=1
y=-1
z=2
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x=-y-z+2
Solve x+y+z=2 for x.
2\left(-y-z+2\right)-3y=5
Substitute -y-z+2 for x in the equation 2x-3y=5.
y=-\frac{2}{5}z-\frac{1}{5} z=-y+1
Solve the second equation for y and the third equation for z.
z=-\left(-\frac{2}{5}z-\frac{1}{5}\right)+1
Substitute -\frac{2}{5}z-\frac{1}{5} for y in the equation z=-y+1.
z=2
Solve z=-\left(-\frac{2}{5}z-\frac{1}{5}\right)+1 for z.
y=-\frac{2}{5}\times 2-\frac{1}{5}
Substitute 2 for z in the equation y=-\frac{2}{5}z-\frac{1}{5}.
y=-1
Calculate y from y=-\frac{2}{5}\times 2-\frac{1}{5}.
x=-\left(-1\right)-2+2
Substitute -1 for y and 2 for z in the equation x=-y-z+2.
x=1
Calculate x from x=-\left(-1\right)-2+2.
x=1 y=-1 z=2
The system is now solved.
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