Solve {l}{0=2*x-14+z}{0=2*y-6+z}{x+2*y-3=0}

$$\left. \begin{array} { l } { 0 = 2 \cdot x - 14 + z } \\ { 0 = 2 \cdot y - 6 + z } \\ { x + 2 \cdot y - 3 = 0 } \end{array} \right.$$

Solve for x, z, y

$$x = \frac{11}{3} = 3\frac{2}{3} \approx 3.666666667$$

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

$$z = \frac{20}{3} = 6\frac{2}{3} \approx 6.666666667$$

Short Steps Using Substitution

Solve 0=2x-14+z for z.

$$z=14-2x$$

Substitute 14-2x for z in the equation 0=2y-6+z.

$$0=2y-6+14-2x$$

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

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

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

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

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

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

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

$$x=4-\frac{1}{3}$$

Calculate x from x=4-\frac{1}{3}.

$$x=\frac{11}{3}$$

Substitute \frac{11}{3} for x in the equation z=14-2x.

$$z=14-2\times \frac{11}{3}$$

Calculate z from z=14-2\times \frac{11}{3}.

$$z=\frac{20}{3}$$

The system is now solved.

$$x=\frac{11}{3} z=\frac{20}{3} y=-\frac{1}{3}$$