Solve {l}{y=x-1/x}{y=10}{z=x}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = \frac{x - 1}{x} }\\ { y = 10 }\\ { z = x }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, x, z, a

$$a=-\frac{1}{9}\approx -0.111111111$$

Solution Steps

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

$$10=\frac{x-1}{x}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$10x=x-1$$

Subtract x from both sides.

$$10x-x=-1$$

Combine 10x and -x to get 9x.

$$9x=-1$$

Divide both sides by 9.

$$x=-\frac{1}{9}$$

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

$$z=-\frac{1}{9}$$

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

$$a=-\frac{1}{9}$$

The system is now solved.

$$y=10 x=-\frac{1}{9} z=-\frac{1}{9} a=-\frac{1}{9}$$