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

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

Solve for x, y, z

$$x=-\frac{1}{3}\approx -0.333333333$$

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

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

Short Steps Using Substitution

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

$$x=-y+2z$$

Substitute -y+2z for x in the second and third equation.

$$-y+2z-y=0 -y+2z+y+z+1=0$$

Solve these equations for y and z respectively.

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

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

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

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

$$x=-\left(-\frac{1}{3}\right)+2\left(-\frac{1}{3}\right)$$

Calculate x from x=-\left(-\frac{1}{3}\right)+2\left(-\frac{1}{3}\right).

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

The system is now solved.

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