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

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

Solve for x, y, z

$$x=2$$

$$y=0$$

$$z=-3$$

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.

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

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

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

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

$$x=2$$

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

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

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

$$y=0$$

Substitute 0 for y and 2 for x in the equation z=-2x+4y+1.

$$z=-2\times 2+4\times 0+1$$

Calculate z from z=-2\times 2+4\times 0+1.

$$z=-3$$

The system is now solved.

$$x=2 y=0 z=-3$$