Solve {c}{2x+2y+z=12P}{3x+5+z=12P61.000}{x+3y+2z=12080.000}

$$\left. \begin{array} { c } { 2 x + 2 y + z = 12 P } \\ { 3 x + 5 + z = 12 P 61.000 } \\ { x + 3 y + 2 z = 12080.000 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{36P-24165}{7}$$

$$y=\frac{60P-12065}{7}$$

$$z=\frac{72460-108P}{7}$$

Short Steps Using Substitution

Solve 2x+2y+z=12P for z.

$$z=-2x-2y+12P$$

Substitute -2x-2y+12P for z in the second and third equation.

$$3x+5-2x-2y+12P=12P_{61}\times 0 x+3y+2\left(-2x-2y+12P\right)=12080$$

Solve these equations for y and x respectively.

$$y=\frac{1}{2}x+\frac{5}{2}+6P x=-\frac{1}{3}y+8P-\frac{12080}{3}$$

Substitute \frac{1}{2}x+\frac{5}{2}+6P for y in the equation x=-\frac{1}{3}y+8P-\frac{12080}{3}.

$$x=-\frac{1}{3}\left(\frac{1}{2}x+\frac{5}{2}+6P\right)+8P-\frac{12080}{3}$$

Solve x=-\frac{1}{3}\left(\frac{1}{2}x+\frac{5}{2}+6P\right)+8P-\frac{12080}{3} for x.

$$x=-\frac{24165}{7}+\frac{36}{7}P$$

Substitute -\frac{24165}{7}+\frac{36}{7}P for x in the equation y=\frac{1}{2}x+\frac{5}{2}+6P.

$$y=\frac{1}{2}\left(-\frac{24165}{7}+\frac{36}{7}P\right)+\frac{5}{2}+6P$$

Calculate y from y=\frac{1}{2}\left(-\frac{24165}{7}+\frac{36}{7}P\right)+\frac{5}{2}+6P.

$$y=-\frac{12065}{7}+\frac{60}{7}P$$

Substitute -\frac{12065}{7}+\frac{60}{7}P for y and -\frac{24165}{7}+\frac{36}{7}P for x in the equation z=-2x-2y+12P.

$$z=-2\left(-\frac{24165}{7}+\frac{36}{7}P\right)-2\left(-\frac{12065}{7}+\frac{60}{7}P\right)+12P$$

Calculate z from z=-2\left(-\frac{24165}{7}+\frac{36}{7}P\right)-2\left(-\frac{12065}{7}+\frac{60}{7}P\right)+12P.

$$z=\frac{72460}{7}-\frac{108}{7}P$$

The system is now solved.

$$x=-\frac{24165}{7}+\frac{36}{7}P y=-\frac{12065}{7}+\frac{60}{7}P z=\frac{72460}{7}-\frac{108}{7}P$$