Solve {l}{66z+17y=z}{21+5z=121}{x+14y=122}

$$\left. \begin{array} { l } { 66 z + 17 y = z } \\ { 21 + 5 z = 121 } \\ { x + 14 y = 122 } \end{array} \right.$$

Solve for z, y, x

$$x = \frac{20274}{17} = 1192\frac{10}{17} \approx 1192.588235294$$

$$y = -\frac{1300}{17} = -76\frac{8}{17} \approx -76.470588235$$

$$z=20$$

Solution Steps

Consider the second equation. Subtract 21 from both sides.

$$5z=121-21$$

Subtract 21 from 121 to get 100.

$$5z=100$$

Divide both sides by 5.

$$z=\frac{100}{5}$$

Divide 100 by 5 to get 20.

$$z=20$$

Consider the first equation. Insert the known values of variables into the equation.

$$66\times 20+17y=20$$

Multiply 66 and 20 to get 1320.

$$1320+17y=20$$

Subtract 1320 from both sides.

$$17y=20-1320$$

Subtract 1320 from 20 to get -1300.

$$17y=-1300$$

Divide both sides by 17.

$$y=-\frac{1300}{17}$$

Consider the third equation. Insert the known values of variables into the equation.

$$x+14\left(-\frac{1300}{17}\right)=122$$

Multiply 14 and -\frac{1300}{17} to get -\frac{18200}{17}.

$$x-\frac{18200}{17}=122$$

Add \frac{18200}{17} to both sides.

$$x=122+\frac{18200}{17}$$

Add 122 and \frac{18200}{17} to get \frac{20274}{17}.

$$x=\frac{20274}{17}$$

The system is now solved.

$$z=20 y=-\frac{1300}{17} x=\frac{20274}{17}$$