Solve {l}{x+y=6}{y+z=8}{x+z=10}

$$\left\{ \begin{array} { l } { x + y = 6 } \\ { y + z = 8 } \\ { x + z = 10 } \end{array} \right.$$

Solve for x, y, z

$$x=4$$

$$y=2$$

$$z=6$$

Short Steps Using Substitution

Solve x+y=6 for x.

$$x=-y+6$$

Substitute -y+6 for x in the equation x+z=10.

$$-y+6+z=10$$

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

$$y=-z+8 z=y+4$$

Substitute -z+8 for y in the equation z=y+4.

$$z=-z+8+4$$

Solve z=-z+8+4 for z.

$$z=6$$

Substitute 6 for z in the equation y=-z+8.

$$y=-6+8$$

Calculate y from y=-6+8.

$$y=2$$

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

$$x=-2+6$$

Calculate x from x=-2+6.

$$x=4$$

The system is now solved.

$$x=4 y=2 z=6$$