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

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

Solve for z, x, y

$$x=-3$$

$$y=1$$

$$z=0$$

Short Steps Using Substitution

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

$$x+y+3\left(3+x\right)+2=0$$

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

$$x=-\frac{1}{4}y-\frac{11}{4} y=-\frac{2}{7}-\frac{3}{7}x$$

Substitute -\frac{1}{4}y-\frac{11}{4} for x in the equation y=-\frac{2}{7}-\frac{3}{7}x.

$$y=-\frac{2}{7}-\frac{3}{7}\left(-\frac{1}{4}y-\frac{11}{4}\right)$$

Solve y=-\frac{2}{7}-\frac{3}{7}\left(-\frac{1}{4}y-\frac{11}{4}\right) for y.

$$y=1$$

Substitute 1 for y in the equation x=-\frac{1}{4}y-\frac{11}{4}.

$$x=-\frac{1}{4}-\frac{11}{4}$$

Calculate x from x=-\frac{1}{4}-\frac{11}{4}.

$$x=-3$$

Substitute -3 for x in the equation z=3+x.

$$z=3-3$$

Calculate z from z=3-3.

$$z=0$$

The system is now solved.

$$z=0 x=-3 y=1$$