Solve {l}{z=12000-(x+y)*50/2400}{x=-2/6*600*(z-0,05)}{y=-2/4*200*(z-0,05)}

$$\left\{ \begin{array} { l } { z = \frac { 12000 - ( x + y ) \cdot 50 } { 2400 } } \\ { x = - \frac { 2 } { 6 } \cdot 600 \cdot ( z - 0,05 ) } \\ { y = - \frac { 2 } { 4 } \cdot 200 \cdot ( z - 0,05 ) } \end{array} \right.$$

Solve for z, x, y

$$x=\frac{1320}{7}\approx 188,571428571$$

$$y=\frac{660}{7}\approx 94,285714286$$

$$z=-\frac{25}{28}\approx -0,892857143$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

$$2400z=12000-50x-50y 6x=-1200z+60 4y=-400z+20$$

Solve 2400z=12000-50x-50y for z.

$$z=5-\frac{1}{48}x-\frac{1}{48}y$$

Substitute 5-\frac{1}{48}x-\frac{1}{48}y for z in the second and third equation.

$$6x=-1200\left(5-\frac{1}{48}x-\frac{1}{48}y\right)+60 4y=-400\left(5-\frac{1}{48}x-\frac{1}{48}y\right)+20$$

Solve these equations for x and y respectively.

$$x=\frac{5940}{19}-\frac{25}{19}y y=\frac{5940}{13}-\frac{25}{13}x$$

Substitute \frac{5940}{19}-\frac{25}{19}y for x in the equation y=\frac{5940}{13}-\frac{25}{13}x.

$$y=\frac{5940}{13}-\frac{25}{13}\left(\frac{5940}{19}-\frac{25}{19}y\right)$$

Solve y=\frac{5940}{13}-\frac{25}{13}\left(\frac{5940}{19}-\frac{25}{19}y\right) for y.

$$y=\frac{660}{7}$$

Substitute \frac{660}{7} for y in the equation x=\frac{5940}{19}-\frac{25}{19}y.

$$x=\frac{5940}{19}-\frac{25}{19}\times \frac{660}{7}$$

Calculate x from x=\frac{5940}{19}-\frac{25}{19}\times \frac{660}{7}.

$$x=\frac{1320}{7}$$

Substitute \frac{1320}{7} for x and \frac{660}{7} for y in the equation z=5-\frac{1}{48}x-\frac{1}{48}y.

$$z=5-\frac{1}{48}\times \frac{1320}{7}-\frac{1}{48}\times \frac{660}{7}$$

Calculate z from z=5-\frac{1}{48}\times \frac{1320}{7}-\frac{1}{48}\times \frac{660}{7}.

$$z=-\frac{25}{28}$$

The system is now solved.

$$z=-\frac{25}{28} x=\frac{1320}{7} y=\frac{660}{7}$$