Solve {l}{2x+y+2z=2}{3x+2y-3z=6}{4x+3y+2z=7}

$$\left. \begin{array} { l } { 2 x + y + 2 z = 2 } \\ { 3 x + 2 y - 3 z = 6 } \\ { 4 x + 3 y + 2 z = 7 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{1}{10}=0.1$$

$$y = \frac{12}{5} = 2\frac{2}{5} = 2.4$$

$$z=-\frac{3}{10}=-0.3$$

Short Steps Using Substitution

Solve 2x+y+2z=2 for y.

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

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

$$3x+2\left(2-2x-2z\right)-3z=6 4x+3\left(2-2x-2z\right)+2z=7$$

Solve these equations for x and z respectively.

$$x=-2-7z z=-\frac{1}{2}x-\frac{1}{4}$$

Substitute -2-7z for x in the equation z=-\frac{1}{2}x-\frac{1}{4}.

$$z=-\frac{1}{2}\left(-2-7z\right)-\frac{1}{4}$$

Solve z=-\frac{1}{2}\left(-2-7z\right)-\frac{1}{4} for z.

$$z=-\frac{3}{10}$$

Substitute -\frac{3}{10} for z in the equation x=-2-7z.

$$x=-2-7\left(-\frac{3}{10}\right)$$

Calculate x from x=-2-7\left(-\frac{3}{10}\right).

$$x=\frac{1}{10}$$

Substitute \frac{1}{10} for x and -\frac{3}{10} for z in the equation y=2-2x-2z.

$$y=2-2\times \frac{1}{10}-2\left(-\frac{3}{10}\right)$$

Calculate y from y=2-2\times \frac{1}{10}-2\left(-\frac{3}{10}\right).

$$y=\frac{12}{5}$$

The system is now solved.

$$x=\frac{1}{10} y=\frac{12}{5} z=-\frac{3}{10}$$