Solve {l}{99y+99x=99}{99z+99y=108}{99x+99z=-72}

$$\left. \begin{array} { l } { 99 y + 99 x = 99 } \\ { 99 z + 99 y = 108 } \\ { 99 x + 99 z = - 72 } \end{array} \right.$$

Solve for y, x, z

$$x=-\frac{9}{22}\approx -0.409090909$$

$$y = \frac{31}{22} = 1\frac{9}{22} \approx 1.409090909$$

$$z=-\frac{7}{22}\approx -0.318181818$$

Short Steps Using Substitution

Solve 99y+99x=99 for y.

$$y=1-x$$

Substitute 1-x for y in the equation 99z+99y=108.

$$99z+99\left(1-x\right)=108$$

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

$$x=-\frac{1}{11}+z z=-\frac{8}{11}-x$$

Substitute -\frac{1}{11}+z for x in the equation z=-\frac{8}{11}-x.

$$z=-\frac{8}{11}-\left(-\frac{1}{11}+z\right)$$

Solve z=-\frac{8}{11}-\left(-\frac{1}{11}+z\right) for z.

$$z=-\frac{7}{22}$$

Substitute -\frac{7}{22} for z in the equation x=-\frac{1}{11}+z.

$$x=-\frac{1}{11}-\frac{7}{22}$$

Calculate x from x=-\frac{1}{11}-\frac{7}{22}.

$$x=-\frac{9}{22}$$

Substitute -\frac{9}{22} for x in the equation y=1-x.

$$y=1-\left(-\frac{9}{22}\right)$$

Calculate y from y=1-\left(-\frac{9}{22}\right).

$$y=\frac{31}{22}$$

The system is now solved.

$$y=\frac{31}{22} x=-\frac{9}{22} z=-\frac{7}{22}$$