Solve {l}{x+y+z=180}{y+3x+8=180}{z+3x-8=180}

$$\left\{ \begin{array} { l } { x + y + z = 180 } \\ { y + 3 x + 8 = 180 } \\ { z + 3 x - 8 = 180 } \end{array} \right.$$

Solve for x, y, z

$$x=36$$

$$y=64$$

$$z=80$$

Short Steps Using Substitution

Solve x+y+z=180 for x.

$$x=-y-z+180$$

Substitute -y-z+180 for x in the second and third equation.

$$y+3\left(-y-z+180\right)+8=180 z+3\left(-y-z+180\right)-8=180$$

Solve these equations for y and z respectively.

$$y=-\frac{3}{2}z+184 z=-\frac{3}{2}y+176$$

Substitute -\frac{3}{2}z+184 for y in the equation z=-\frac{3}{2}y+176.

$$z=-\frac{3}{2}\left(-\frac{3}{2}z+184\right)+176$$

Solve z=-\frac{3}{2}\left(-\frac{3}{2}z+184\right)+176 for z.

$$z=80$$

Substitute 80 for z in the equation y=-\frac{3}{2}z+184.

$$y=-\frac{3}{2}\times 80+184$$

Calculate y from y=-\frac{3}{2}\times 80+184.

$$y=64$$

Substitute 64 for y and 80 for z in the equation x=-y-z+180.

$$x=-64-80+180$$

Calculate x from x=-64-80+180.

$$x=36$$

The system is now solved.

$$x=36 y=64 z=80$$