Solve {l}{x+y=8}{y+z=12}{z+x=5}

$$\left. \begin{array} { l } { x + y = 8 } \\ { y + z = 12 } \\ { z + x = 5 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{1}{2}=0.5$$

$$y = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

$$z = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Short Steps Using Substitution

Solve x+y=8 for x.

$$x=-y+8$$

Substitute -y+8 for x in the equation z+x=5.

$$z-y+8=5$$

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

$$y=-z+12 z=y-3$$

Substitute -z+12 for y in the equation z=y-3.

$$z=-z+12-3$$

Solve z=-z+12-3 for z.

$$z=\frac{9}{2}$$

Substitute \frac{9}{2} for z in the equation y=-z+12.

$$y=-\frac{9}{2}+12$$

Calculate y from y=-\frac{9}{2}+12.

$$y=\frac{15}{2}$$

Substitute \frac{15}{2} for y in the equation x=-y+8.

$$x=-\frac{15}{2}+8$$

Calculate x from x=-\frac{15}{2}+8.

$$x=\frac{1}{2}$$

The system is now solved.

$$x=\frac{1}{2} y=\frac{15}{2} z=\frac{9}{2}$$