Solve {l}{x+x+z=-1}{3x+3y-3z=-3}{2x-3y+z=1}

$$\left. \begin{array} { l } { x + x + z = - 1 } \\ { 3 x + 3 y - 3 z = - 3 } \\ { 2 x - 3 y + z = 1 } \end{array} \right.$$

Solve for x, z, y

$$x=-\frac{4}{9}\approx -0.444444444$$

$$y=-\frac{2}{3}\approx -0.666666667$$

$$z=-\frac{1}{9}\approx -0.111111111$$

Short Steps Using Substitution

Solve x+x+z=-1 for z.

$$z=-2x-1$$

Substitute -2x-1 for z in the second and third equation.

$$3x+3y-3\left(-2x-1\right)=-3 2x-3y-2x-1=1$$

Solve these equations for x and y respectively.

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

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

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

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

$$x=-\frac{4}{9}$$

Substitute -\frac{4}{9} for x in the equation z=-2x-1.

$$z=-2\left(-\frac{4}{9}\right)-1$$

Calculate z from z=-2\left(-\frac{4}{9}\right)-1.

$$z=-\frac{1}{9}$$

The system is now solved.

$$x=-\frac{4}{9} z=-\frac{1}{9} y=-\frac{2}{3}$$