Solve {l}{x+y=5}{x-z=3}{x+z=8}

$$\left\{ \begin{array} { l } { x + y = 5 } \\ { x - z = 3 } \\ { x + z = 8 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

$$y=-\frac{1}{2}=-0.5$$

$$z = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Short Steps Using Substitution

Solve x+y=5 for x.

$$x=-y+5$$

Substitute -y+5 for x in the second and third equation.

$$-y+5-z=3 -y+5+z=8$$

Solve these equations for y and z respectively.

$$y=2-z z=y+3$$

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

$$z=2-z+3$$

Solve z=2-z+3 for z.

$$z=\frac{5}{2}$$

Substitute \frac{5}{2} for z in the equation y=2-z.

$$y=2-\frac{5}{2}$$

Calculate y from y=2-\frac{5}{2}.

$$y=-\frac{1}{2}$$

Substitute -\frac{1}{2} for y in the equation x=-y+5.

$$x=-\left(-\frac{1}{2}\right)+5$$

Calculate x from x=-\left(-\frac{1}{2}\right)+5.

$$x=\frac{11}{2}$$

The system is now solved.

$$x=\frac{11}{2} y=-\frac{1}{2} z=\frac{5}{2}$$