Solve {l}{x+y+z=5-x}{4x=4+z-y}{2(x+y)+z=8}

$$\left\{ \begin{array} { l } { x + y + z = 5 - x } \\ { 4 x = 4 + z - y } \\ { 2 ( x + y ) + z = 8 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{1}{2}=0.5$$

$$y=3$$

$$z=1$$

Short Steps Using Substitution

Solve x+y+z=5-x for y.

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

Substitute -2x-z+5 for y in the second and third equation.

$$4x=4+z-\left(-2x-z+5\right) 2\left(x-2x-z+5\right)+z=8$$

Solve these equations for x and z respectively.

$$x=-\frac{1}{2}+z z=-2x+2$$

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

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

Solve z=-2\left(-\frac{1}{2}+z\right)+2 for z.

$$z=1$$

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

$$x=-\frac{1}{2}+1$$

Calculate x from x=-\frac{1}{2}+1.

$$x=\frac{1}{2}$$

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

$$y=-2\times \frac{1}{2}-1+5$$

Calculate y from y=-2\times \frac{1}{2}-1+5.

$$y=3$$

The system is now solved.

$$x=\frac{1}{2} y=3 z=1$$