Solve {l}{1/2x+1/7y=1/3z}{40z=532x}{0.232y=1/4z}

$$\left\{ \begin{array} { l } { \frac { 1 } { 2 } x + \frac { 1 } { 7 } y = \frac { 1 } { 3 } z } \\ { 40 z = 532 x } \\ { 0.232 y = \frac { 1 } { 4 } z } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve \frac{1}{2}x+\frac{1}{7}y=\frac{1}{3}z for x.

$$x=-\frac{2}{7}y+\frac{2}{3}z$$

Substitute -\frac{2}{7}y+\frac{2}{3}z for x in the equation 40z=532x.

$$40z=532\left(-\frac{2}{7}y+\frac{2}{3}z\right)$$

Solve the second equation for y and the third equation for z.

$$y=\frac{118}{57}z z=0.928y$$

Substitute \frac{118}{57}z for y in the equation z=0.928y.

$$z=0.928\times \frac{118}{57}z$$

Solve z=0.928\times \frac{118}{57}z for z.

$$z=0$$

Substitute 0 for z in the equation y=\frac{118}{57}z.

$$y=\frac{118}{57}\times 0$$

Calculate y from y=\frac{118}{57}\times 0.

$$y=0$$

Substitute 0 for y and 0 for z in the equation x=-\frac{2}{7}y+\frac{2}{3}z.

$$x=-\frac{2}{7}\times 0+\frac{2}{3}\times 0$$

Calculate x from x=-\frac{2}{7}\times 0+\frac{2}{3}\times 0.

$$x=0$$

The system is now solved.

$$x=0 y=0 z=0$$