Solve {l}{x+y=5}{y+z=-2}{x+z=3}

$$\left\{ \begin{array} { l } { x + y = 5 } \\ { y + z = - 2 } \\ { x + z = 3 } \end{array} \right.$$

Solve for x, y, z

$$x=5$$

$$y=0$$

$$z=-2$$

Short Steps Using Substitution

Solve x+y=5 for x.

$$x=-y+5$$

Substitute -y+5 for x in the equation x+z=3.

$$-y+5+z=3$$

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

$$y=-2-z z=y-2$$

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

$$z=-2-z-2$$

Solve z=-2-z-2 for z.

$$z=-2$$

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

$$y=-2-\left(-2\right)$$

Calculate y from y=-2-\left(-2\right).

$$y=0$$

Substitute 0 for y in the equation x=-y+5.

$$x=-0+5$$

Calculate x from x=-0+5.

$$x=5$$

The system is now solved.

$$x=5 y=0 z=-2$$