Solve {l}{7x+7y+z=1}{x+8y+8z=8}{9x+y+9z=9}

$$\left. \begin{array} { l } { 7 x + 7 y + z = 1 } \\ { x + 8 y + 8 z = 8 } \\ { 9 x + y + 9 z = 9 } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=1$$

Short Steps Using Substitution

Solve 7x+7y+z=1 for z.

$$z=-7x-7y+1$$

Substitute -7x-7y+1 for z in the second and third equation.

$$x+8y+8\left(-7x-7y+1\right)=8 9x+y+9\left(-7x-7y+1\right)=9$$

Solve these equations for y and x respectively.

$$y=-\frac{55}{48}x x=-\frac{31}{27}y$$

Substitute -\frac{55}{48}x for y in the equation x=-\frac{31}{27}y.

$$x=-\frac{31}{27}\left(-\frac{55}{48}\right)x$$

Solve x=-\frac{31}{27}\left(-\frac{55}{48}\right)x for x.

$$x=0$$

Substitute 0 for x in the equation y=-\frac{55}{48}x.

$$y=-\frac{55}{48}\times 0$$

Calculate y from y=-\frac{55}{48}\times 0.

$$y=0$$

Substitute 0 for y and 0 for x in the equation z=-7x-7y+1.

$$z=-7\times 0-7\times 0+1$$

Calculate z from z=-7\times 0-7\times 0+1.

$$z=1$$

The system is now solved.

$$x=0 y=0 z=1$$