Solve {l}{x+y-1=0}{x-z=0}{x-y+z=1}

$$\left\{ \begin{array} { l } { x + y - 1 = 0 } \\ { x - z = 0 } \\ { x - y + z = 1 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{2}{3}\approx 0.666666667$$

$$y=\frac{1}{3}\approx 0.333333333$$

$$z=\frac{2}{3}\approx 0.666666667$$

Short Steps Using Substitution

Solve x+y-1=0 for x.

$$x=-y+1$$

Substitute -y+1 for x in the second and third equation.

$$-y+1-z=0 -y+1-y+z=1$$

Solve these equations for y and z respectively.

$$y=1-z z=2y$$

Substitute 1-z for y in the equation z=2y.

$$z=2\left(1-z\right)$$

Solve z=2\left(1-z\right) for z.

$$z=\frac{2}{3}$$

Substitute \frac{2}{3} for z in the equation y=1-z.

$$y=1-\frac{2}{3}$$

Calculate y from y=1-\frac{2}{3}.

$$y=\frac{1}{3}$$

Substitute \frac{1}{3} for y in the equation x=-y+1.

$$x=-\frac{1}{3}+1$$

Calculate x from x=-\frac{1}{3}+1.

$$x=\frac{2}{3}$$

The system is now solved.

$$x=\frac{2}{3} y=\frac{1}{3} z=\frac{2}{3}$$