Solve {l}{2y+1/2=1}{2y+1/2x=2}

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

Solve for y, x

$$x=\frac{1}{3}\approx 0.333333333$$

$$y=\frac{1}{4}=0.25$$

Solution Steps

Consider the first equation. Subtract \frac{1}{2} from both sides.

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

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

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

Divide both sides by 2.

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

Express \frac{\frac{1}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

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

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

$$2\times \frac{1}{4}+\frac{1}{2x}=2$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x, the least common multiple of 4,2x.

$$2\times \frac{1}{4}\times 4x+2=8x$$

Multiply 2 and \frac{1}{4} to get \frac{1}{2}.

$$\frac{1}{2}\times 4x+2=8x$$

Multiply \frac{1}{2} and 4 to get 2.

$$2x+2=8x$$

Subtract 8x from both sides.

$$2x+2-8x=0$$

Combine 2x and -8x to get -6x.

$$-6x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-6x=-2$$

Divide both sides by -6.

$$x=\frac{-2}{-6}$$

Reduce the fraction \frac{-2}{-6} to lowest terms by extracting and canceling out -2.

$$x=\frac{1}{3}$$

The system is now solved.

$$y=\frac{1}{4} x=\frac{1}{3}$$