Solve {l}{-2x+4y-z=1}{x+7y+2z=-4}{3x-2y+3z=-3}

$$\left. \begin{array}{l}{ - 2 x + 4 y - z = 1 }\\{ x + 7 y + 2 z = - 4 }\\{ 3 x - 2 y + 3 z = - 3 }\end{array} \right.$$

Solve for x, y, z

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

$$y=-\frac{2}{5}=-0.4$$

$$z=\frac{1}{15}\approx 0.066666667$$

Short Steps Using Substitution

Solve -2x+4y-z=1 for z.

$$z=-2x+4y-1$$

Substitute -2x+4y-1 for z in the second and third equation.

$$x+7y+2\left(-2x+4y-1\right)=-4 3x-2y+3\left(-2x+4y-1\right)=-3$$

Solve these equations for y and x respectively.

$$y=\frac{1}{5}x-\frac{2}{15} x=\frac{10}{3}y$$

Substitute \frac{1}{5}x-\frac{2}{15} for y in the equation x=\frac{10}{3}y.

$$x=\frac{10}{3}\left(\frac{1}{5}x-\frac{2}{15}\right)$$

Solve x=\frac{10}{3}\left(\frac{1}{5}x-\frac{2}{15}\right) for x.

$$x=-\frac{4}{3}$$

Substitute -\frac{4}{3} for x in the equation y=\frac{1}{5}x-\frac{2}{15}.

$$y=\frac{1}{5}\left(-\frac{4}{3}\right)-\frac{2}{15}$$

Calculate y from y=\frac{1}{5}\left(-\frac{4}{3}\right)-\frac{2}{15}.

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

Substitute -\frac{2}{5} for y and -\frac{4}{3} for x in the equation z=-2x+4y-1.

$$z=-2\left(-\frac{4}{3}\right)+4\left(-\frac{2}{5}\right)-1$$

Calculate z from z=-2\left(-\frac{4}{3}\right)+4\left(-\frac{2}{5}\right)-1.

$$z=\frac{1}{15}$$

The system is now solved.

$$x=-\frac{4}{3} y=-\frac{2}{5} z=\frac{1}{15}$$