Solve {l}{x-z-2=0}{3x-6y-7=0}{3y+3z-4=0}

$$\left\{ \begin{array} { l } { x - z - 2 = 0 } \\ { 3 x - 6 y - 7 = 0 } \\ { 3 y + 3 z - 4 = 0 } \end{array} \right.$$

Solve for x, z, y

$$x=3$$

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

$$z=1$$

Short Steps Using Substitution

Solve x-z-2=0 for x.

$$x=z+2$$

Substitute z+2 for x in the equation 3x-6y-7=0.

$$3\left(z+2\right)-6y-7=0$$

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

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

Substitute \frac{1}{3}+2y for z in the equation y=-z+\frac{4}{3}.

$$y=-\left(\frac{1}{3}+2y\right)+\frac{4}{3}$$

Solve y=-\left(\frac{1}{3}+2y\right)+\frac{4}{3} for y.

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

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

$$z=\frac{1}{3}+2\times \frac{1}{3}$$

Calculate z from z=\frac{1}{3}+2\times \frac{1}{3}.

$$z=1$$

Substitute 1 for z in the equation x=z+2.

$$x=1+2$$

Calculate x from x=1+2.

$$x=3$$

The system is now solved.

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