Solve {l}{x+z=y}{7z=x+y+2}{x+y+z=14}

$$\left. \begin{array} { l } { x + z = y } \\ { 7 z = x + y + 2 } \\ { x + y + z = 14 } \end{array} \right.$$

Solve for x, z, y

$$x=5$$

$$y=7$$

$$z=2$$

Short Steps Using Substitution

Solve x+z=y for y.

$$y=x+z$$

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

$$7z=x+x+z+2 x+x+z+z=14$$

Solve these equations for z and x respectively.

$$z=\frac{1}{3}+\frac{1}{3}x x=7-z$$

Substitute \frac{1}{3}+\frac{1}{3}x for z in the equation x=7-z.

$$x=7-\left(\frac{1}{3}+\frac{1}{3}x\right)$$

Solve x=7-\left(\frac{1}{3}+\frac{1}{3}x\right) for x.

$$x=5$$

Substitute 5 for x in the equation z=\frac{1}{3}+\frac{1}{3}x.

$$z=\frac{1}{3}+\frac{1}{3}\times 5$$

Calculate z from z=\frac{1}{3}+\frac{1}{3}\times 5.

$$z=2$$

Substitute 2 for z and 5 for x in the equation y=x+z.

$$y=5+2$$

Calculate y from y=5+2.

$$y=7$$

The system is now solved.

$$x=5 z=2 y=7$$