Solve {l}{1/8{(x-6)}=1+x}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{1}{8} {(x - 6)} = 1 + x }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-2$$

Solution Steps

Consider the first equation. Use the distributive property to multiply \frac{1}{8} by x-6.

$$\frac{1}{8}x-\frac{3}{4}=1+x$$

Subtract x from both sides.

$$\frac{1}{8}x-\frac{3}{4}-x=1$$

Combine \frac{1}{8}x and -x to get -\frac{7}{8}x.

$$-\frac{7}{8}x-\frac{3}{4}=1$$

Add \frac{3}{4} to both sides.

$$-\frac{7}{8}x=1+\frac{3}{4}$$

Add 1 and \frac{3}{4} to get \frac{7}{4}.

$$-\frac{7}{8}x=\frac{7}{4}$$

Multiply both sides by -\frac{8}{7}, the reciprocal of -\frac{7}{8}.

$$x=\frac{7}{4}\left(-\frac{8}{7}\right)$$

Multiply \frac{7}{4} and -\frac{8}{7} to get -2.

$$x=-2$$

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

$$y=-2$$

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

$$z=-2$$

The system is now solved.

$$x=-2 y=-2 z=-2$$