Solve {l}{1/2x-1-2x=y}{x=1/31/3}

$$\left\{ \begin{array} { l } { \frac { 1 } { 2 x - 1 } - 2 x = y } \\ { x = \frac { 1 } { 3 } \frac { 1 } { 3 } } \end{array} \right.$$

Solve for x, y

$$x=\frac{1}{9}\approx 0.111111111$$

$$y = -\frac{95}{63} = -1\frac{32}{63} \approx -1.507936508$$

Solution Steps

Consider the second equation. Multiply \frac{1}{3} and \frac{1}{3} to get \frac{1}{9}.

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

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

$$\frac{1}{2\times \frac{1}{9}-1}-2\times \frac{1}{9}=y$$

Multiply 2 and \frac{1}{9} to get \frac{2}{9}.

$$\frac{1}{\frac{2}{9}-1}-2\times \frac{1}{9}=y$$

Subtract 1 from \frac{2}{9} to get -\frac{7}{9}.

$$\frac{1}{-\frac{7}{9}}-2\times \frac{1}{9}=y$$

Divide 1 by -\frac{7}{9} by multiplying 1 by the reciprocal of -\frac{7}{9}.

$$1\left(-\frac{9}{7}\right)-2\times \frac{1}{9}=y$$

Multiply 1 and -\frac{9}{7} to get -\frac{9}{7}.

$$-\frac{9}{7}-2\times \frac{1}{9}=y$$

Multiply -2 and \frac{1}{9} to get -\frac{2}{9}.

$$-\frac{9}{7}-\frac{2}{9}=y$$

Subtract \frac{2}{9} from -\frac{9}{7} to get -\frac{95}{63}.

$$-\frac{95}{63}=y$$

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

$$y=-\frac{95}{63}$$

The system is now solved.

$$x=\frac{1}{9} y=-\frac{95}{63}$$