Solve {l}{x-1/x=20}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{x - 1}{x} = 20 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-\frac{1}{19}\approx -0.052631579$$

Solution Steps

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

$$x-1=20x$$

Subtract 20x from both sides.

$$x-1-20x=0$$

Combine x and -20x to get -19x.

$$-19x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$-19x=1$$

Divide both sides by -19.

$$x=-\frac{1}{19}$$

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

$$y=-\frac{1}{19}$$

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

$$z=-\frac{1}{19}$$

The system is now solved.

$$x=-\frac{1}{19} y=-\frac{1}{19} z=-\frac{1}{19}$$