Solve {l}{-6/{(x-10)}=6}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { -6 / {(x - 10)} = 6 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=9$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 10 since division by zero is not defined. Multiply both sides of the equation by x-10.

$$-6=6\left(x-10\right)$$

Use the distributive property to multiply 6 by x-10.

$$-6=6x-60$$

Swap sides so that all variable terms are on the left hand side.

$$6x-60=-6$$

Add 60 to both sides.

$$6x=-6+60$$

Add -6 and 60 to get 54.

$$6x=54$$

Divide both sides by 6.

$$x=\frac{54}{6}$$

Divide 54 by 6 to get 9.

$$x=9$$

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

$$y=9$$

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

$$z=9$$

The system is now solved.

$$x=9 y=9 z=9$$