Solve {l}{y=2/x-1/x^2}{x=1/2}

$$\left\{ \begin{array} { l } { y = \frac { 2 } { x } - \frac { 1 } { x ^ { 2 } } } \\ { x = \frac { 1 } { 2 } } \end{array} \right.$$

Solve for y, x

$$x=\frac{1}{2}=0.5$$

$$y=0$$

Solution Steps

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

$$y=\frac{2}{\frac{1}{2}}-\frac{1}{\left(\frac{1}{2}\right)^{2}}$$

Divide 2 by \frac{1}{2} by multiplying 2 by the reciprocal of \frac{1}{2}.

$$y=2\times 2-\frac{1}{\left(\frac{1}{2}\right)^{2}}$$

Multiply 2 and 2 to get 4.

$$y=4-\frac{1}{\left(\frac{1}{2}\right)^{2}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$y=4-\frac{1}{\frac{1}{4}}$$

Divide 1 by \frac{1}{4} by multiplying 1 by the reciprocal of \frac{1}{4}.

$$y=4-1\times 4$$

Multiply 1 and 4 to get 4.

$$y=4-4$$

Subtract 4 from 4 to get 0.

$$y=0$$

The system is now solved.

$$y=0 x=\frac{1}{2}$$