Solve {l}{x+y+z=108}{.25x+.4y+-85z=48.6}{z=2y}

$$\left. \begin{array}{l}{ x + y + z = 108 }\\{ .25 x + .4 y + - 85 z = 48.6 }\\{ z = 2 y }\end{array} \right.$$

Solve for x, y, z

$$x = \frac{369252}{3407} = 108\frac{1296}{3407} \approx 108.380393308$$

$$y=-\frac{432}{3407}\approx -0.126797769$$

$$z=-\frac{864}{3407}\approx -0.253595539$$

Short Steps Using Substitution

Reorder the equations.

$$z=2y 0.25x+0.4y-85z=48.6 x+y+z=108$$

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

$$0.25x+0.4y-85\times 2y=48.6 x+y+2y=108$$

Solve these equations for y and x respectively.

$$y=\frac{5}{3392}x-\frac{243}{848} x=108-3y$$

Substitute \frac{5}{3392}x-\frac{243}{848} for y in the equation x=108-3y.

$$x=108-3\left(\frac{5}{3392}x-\frac{243}{848}\right)$$

Solve x=108-3\left(\frac{5}{3392}x-\frac{243}{848}\right) for x.

$$x=\frac{369252}{3407}$$

Substitute \frac{369252}{3407} for x in the equation y=\frac{5}{3392}x-\frac{243}{848}.

$$y=\frac{5}{3392}\times \frac{369252}{3407}-\frac{243}{848}$$

Calculate y from y=\frac{5}{3392}\times \frac{369252}{3407}-\frac{243}{848}.

$$y=-\frac{432}{3407}$$

Substitute -\frac{432}{3407} for y in the equation z=2y.

$$z=2\left(-\frac{432}{3407}\right)$$

Calculate z from z=2\left(-\frac{432}{3407}\right).

$$z=-\frac{864}{3407}$$

The system is now solved.

$$x=\frac{369252}{3407} y=-\frac{432}{3407} z=-\frac{864}{3407}$$