Solve {l}{x+y+z=18}{2x+z=4}{2y+2x=10}

$$\left. \begin{array} { l } { x + y + z = 18 } \\ { 2 x + z = 4 } \\ { 2 y + 2 x = 10 } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

$$y = \frac{19}{2} = 9\frac{1}{2} = 9.5$$

$$z=13$$

Short Steps Using Substitution

Solve x+y+z=18 for x.

$$x=-y-z+18$$

Substitute -y-z+18 for x in the second and third equation.

$$2\left(-y-z+18\right)+z=4 2y+2\left(-y-z+18\right)=10$$

Solve these equations for y and z respectively.

$$y=16-\frac{1}{2}z z=13$$

Substitute 13 for z in the equation y=16-\frac{1}{2}z.

$$y=16-\frac{1}{2}\times 13$$

Calculate y from y=16-\frac{1}{2}\times 13.

$$y=\frac{19}{2}$$

Substitute \frac{19}{2} for y and 13 for z in the equation x=-y-z+18.

$$x=-\frac{19}{2}-13+18$$

Calculate x from x=-\frac{19}{2}-13+18.

$$x=-\frac{9}{2}$$

The system is now solved.

$$x=-\frac{9}{2} y=\frac{19}{2} z=13$$