Solve {l}{x+2y+62=05quad(1)}{-x+y-2z=3}{x-4y-2z=1}

$$\left\{ \begin{array} { l } { x + 2 y + 62 = 05 \quad ( 1 ) } \\ { - x + y - 2 z = 3 } \\ { x - 4 y - 2 z = 1 } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{289}{9} = -32\frac{1}{9} \approx -32.111111111$$

$$y = -\frac{112}{9} = -12\frac{4}{9} \approx -12.444444444$$

$$z = \frac{25}{3} = 8\frac{1}{3} \approx 8.333333333$$

Short Steps Using Substitution

Solve x+2y+62=5\times 1 for x.

$$x=-2y-57$$

Substitute -2y-57 for x in the second and third equation.

$$-\left(-2y-57\right)+y-2z=3 -2y-57-4y-2z=1$$

Solve these equations for y and z respectively.

$$y=-18+\frac{2}{3}z z=-29-3y$$

Substitute -18+\frac{2}{3}z for y in the equation z=-29-3y.

$$z=-29-3\left(-18+\frac{2}{3}z\right)$$

Solve z=-29-3\left(-18+\frac{2}{3}z\right) for z.

$$z=\frac{25}{3}$$

Substitute \frac{25}{3} for z in the equation y=-18+\frac{2}{3}z.

$$y=-18+\frac{2}{3}\times \frac{25}{3}$$

Calculate y from y=-18+\frac{2}{3}\times \frac{25}{3}.

$$y=-\frac{112}{9}$$

Substitute -\frac{112}{9} for y in the equation x=-2y-57.

$$x=-2\left(-\frac{112}{9}\right)-57$$

Calculate x from x=-2\left(-\frac{112}{9}\right)-57.

$$x=-\frac{289}{9}$$

The system is now solved.

$$x=-\frac{289}{9} y=-\frac{112}{9} z=\frac{25}{3}$$