Solve {l}{x+1-2y=0}{y+z-2=0}{2x+y-z-6=0}

$$\left\{ \begin{array} { l } { x + 1 - 2 y = 0 } \\ { y + z - 2 = 0 } \\ { 2 x + y - z - 6 = 0 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

$$y = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

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

Short Steps Using Substitution

Solve x+1-2y=0 for x.

$$x=-1+2y$$

Substitute -1+2y for x in the equation 2x+y-z-6=0.

$$2\left(-1+2y\right)+y-z-6=0$$

Solve the second equation for y and the third equation for z.

$$y=-z+2 z=-8+5y$$

Substitute -z+2 for y in the equation z=-8+5y.

$$z=-8+5\left(-z+2\right)$$

Solve z=-8+5\left(-z+2\right) for z.

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

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

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

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

$$y=\frac{5}{3}$$

Substitute \frac{5}{3} for y in the equation x=-1+2y.

$$x=-1+2\times \frac{5}{3}$$

Calculate x from x=-1+2\times \frac{5}{3}.

$$x=\frac{7}{3}$$

The system is now solved.

$$x=\frac{7}{3} y=\frac{5}{3} z=\frac{1}{3}$$