Solve {l}{1/x-6+2=x/x-6}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{1}{x - 6} + 2 = \frac{x}{x - 6} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=11$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$1+\left(x-6\right)\times 2=x$$

Use the distributive property to multiply x-6 by 2.

$$1+2x-12=x$$

Subtract 12 from 1 to get -11.

$$-11+2x=x$$

Subtract x from both sides.

$$-11+2x-x=0$$

Combine 2x and -x to get x.

$$-11+x=0$$

Add 11 to both sides. Anything plus zero gives itself.

$$x=11$$

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

$$y=11$$

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

$$z=11$$

The system is now solved.

$$x=11 y=11 z=11$$