Solve {l}{x+y=3}{x+z=4}{z+y=5}

$$\left\{ \begin{array} { l } { x + y = 3 } \\ { x + z = 4 } \\ { z + y = 5 } \end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=2$$

$$z=3$$

Short Steps Using Substitution

Solve x+y=3 for x.

$$x=-y+3$$

Substitute -y+3 for x in the equation x+z=4.

$$-y+3+z=4$$

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

$$y=-1+z z=-y+5$$

Substitute -1+z for y in the equation z=-y+5.

$$z=-\left(-1+z\right)+5$$

Solve z=-\left(-1+z\right)+5 for z.

$$z=3$$

Substitute 3 for z in the equation y=-1+z.

$$y=-1+3$$

Calculate y from y=-1+3.

$$y=2$$

Substitute 2 for y in the equation x=-y+3.

$$x=-2+3$$

Calculate x from x=-2+3.

$$x=1$$

The system is now solved.

$$x=1 y=2 z=3$$