Solve {l}{x/1+x=y}{x=1/2008}

$$\left. \begin{array} { l } { \frac { x } { 1 + x } = y } \\ { x = \frac { 1 } { 2008 } } \end{array} \right.$$

Solve for x, y

$$x=\frac{1}{2008}\approx 0.000498008$$

$$y=\frac{1}{2009}\approx 0.00049776$$

Solution Steps

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

$$\frac{\frac{1}{2008}}{1+\frac{1}{2008}}=y$$

Add 1 and \frac{1}{2008} to get \frac{2009}{2008}.

$$\frac{\frac{1}{2008}}{\frac{2009}{2008}}=y$$

Divide \frac{1}{2008} by \frac{2009}{2008} by multiplying \frac{1}{2008} by the reciprocal of \frac{2009}{2008}.

$$\frac{1}{2008}\times \frac{2008}{2009}=y$$

Multiply \frac{1}{2008} and \frac{2008}{2009} to get \frac{1}{2009}.

$$\frac{1}{2009}=y$$

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

$$y=\frac{1}{2009}$$

The system is now solved.

$$x=\frac{1}{2008} y=\frac{1}{2009}$$