Solve {l}{x+y=15}{y=5-z}{x+z=20}

$$\left\{ \begin{array} { l } { x + y = 15 } \\ { y = 5 - z } \\ { x + z = 20 } \end{array} \right.$$

Solve for x, y, z

$$x=15$$

$$y=0$$

$$z=5$$

Short Steps Using Substitution

Reorder the equations.

$$y=5-z x+y=15 x+z=20$$

Substitute 5-z for y in the equation x+y=15.

$$x+5-z=15$$

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

$$x=10+z z=-x+20$$

Substitute 10+z for x in the equation z=-x+20.

$$z=-\left(10+z\right)+20$$

Solve z=-\left(10+z\right)+20 for z.

$$z=5$$

Substitute 5 for z in the equation x=10+z.

$$x=10+5$$

Calculate x from x=10+5.

$$x=15$$

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

$$y=5-5$$

Calculate y from y=5-5.

$$y=0$$

The system is now solved.

$$x=15 y=0 z=5$$