Solve {l}{x+y=5}{y+z=6}{z+x=7}

$$\left\{ \begin{array} { l } { x + y = 5 } \\ { y + z = 6 } \\ { z + x = 7 } \end{array} \right.$$

Solve for x, y, z

$$x=3$$

$$y=2$$

$$z=4$$

Short Steps Using Substitution

Solve x+y=5 for x.

$$x=-y+5$$

Substitute -y+5 for x in the equation z+x=7.

$$z-y+5=7$$

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

$$y=-z+6 z=y+2$$

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

$$z=-z+6+2$$

Solve z=-z+6+2 for z.

$$z=4$$

Substitute 4 for z in the equation y=-z+6.

$$y=-4+6$$

Calculate y from y=-4+6.

$$y=2$$

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

$$x=-2+5$$

Calculate x from x=-2+5.

$$x=3$$

The system is now solved.

$$x=3 y=2 z=4$$