Solve y+1/3/3+frac{1{3}}=x+2/3/2+frac{2{3}}

$$\frac { y + \frac { 1 } { 3 } } { 3 + \frac { 1 } { 3 } } = \frac { x + \frac { 2 } { 3 } } { 2 + \frac { 2 } { 3 } }$$

Solve for x

$$x=\frac{4y-2}{5}$$

Steps for Solving Linear Equation

Add 3 and \frac{1}{3} to get \frac{10}{3}.

$$\frac{y+\frac{1}{3}}{\frac{10}{3}}=\frac{x+\frac{2}{3}}{2+\frac{2}{3}}$$

Add 2 and \frac{2}{3} to get \frac{8}{3}.

$$\frac{y+\frac{1}{3}}{\frac{10}{3}}=\frac{x+\frac{2}{3}}{\frac{8}{3}}$$

Divide each term of y+\frac{1}{3} by \frac{10}{3} to get \frac{y}{\frac{10}{3}}+\frac{\frac{1}{3}}{\frac{10}{3}}.

$$\frac{y}{\frac{10}{3}}+\frac{\frac{1}{3}}{\frac{10}{3}}=\frac{x+\frac{2}{3}}{\frac{8}{3}}$$

Divide \frac{1}{3} by \frac{10}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{10}{3}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{3}\times \frac{3}{10}=\frac{x+\frac{2}{3}}{\frac{8}{3}}$$

Multiply \frac{1}{3} and \frac{3}{10} to get \frac{1}{10}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{10}=\frac{x+\frac{2}{3}}{\frac{8}{3}}$$

Divide each term of x+\frac{2}{3} by \frac{8}{3} to get \frac{x}{\frac{8}{3}}+\frac{\frac{2}{3}}{\frac{8}{3}}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{10}=\frac{x}{\frac{8}{3}}+\frac{\frac{2}{3}}{\frac{8}{3}}$$

Divide \frac{2}{3} by \frac{8}{3} by multiplying \frac{2}{3} by the reciprocal of \frac{8}{3}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{10}=\frac{x}{\frac{8}{3}}+\frac{2}{3}\times \frac{3}{8}$$

Multiply \frac{2}{3} and \frac{3}{8} to get \frac{1}{4}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{10}=\frac{x}{\frac{8}{3}}+\frac{1}{4}$$

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

$$\frac{x}{\frac{8}{3}}+\frac{1}{4}=\frac{y}{\frac{10}{3}}+\frac{1}{10}$$

Subtract \frac{1}{4} from both sides.

$$\frac{x}{\frac{8}{3}}=\frac{y}{\frac{10}{3}}+\frac{1}{10}-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{1}{10} to get -\frac{3}{20}.

$$\frac{x}{\frac{8}{3}}=\frac{y}{\frac{10}{3}}-\frac{3}{20}$$

The equation is in standard form.

$$\frac{3}{8}x=\frac{3y}{10}-\frac{3}{20}$$

Divide both sides of the equation by \frac{3}{8}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{8}x}{\frac{3}{8}}=\frac{\frac{3y}{10}-\frac{3}{20}}{\frac{3}{8}}$$

Dividing by \frac{3}{8} undoes the multiplication by \frac{3}{8}.

$$x=\frac{\frac{3y}{10}-\frac{3}{20}}{\frac{3}{8}}$$

Divide \frac{3y}{10}-\frac{3}{20} by \frac{3}{8} by multiplying \frac{3y}{10}-\frac{3}{20} by the reciprocal of \frac{3}{8}.

$$x=\frac{4y-2}{5}$$

Solve for y

$$y=\frac{5x}{4}+\frac{1}{2}$$

Steps for Solving Linear Equation

Add 3 and \frac{1}{3} to get \frac{10}{3}.

$$\frac{y+\frac{1}{3}}{\frac{10}{3}}=\frac{x+\frac{2}{3}}{2+\frac{2}{3}}$$

Add 2 and \frac{2}{3} to get \frac{8}{3}.

$$\frac{y+\frac{1}{3}}{\frac{10}{3}}=\frac{x+\frac{2}{3}}{\frac{8}{3}}$$

Divide each term of y+\frac{1}{3} by \frac{10}{3} to get \frac{y}{\frac{10}{3}}+\frac{\frac{1}{3}}{\frac{10}{3}}.

$$\frac{y}{\frac{10}{3}}+\frac{\frac{1}{3}}{\frac{10}{3}}=\frac{x+\frac{2}{3}}{\frac{8}{3}}$$

Divide \frac{1}{3} by \frac{10}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{10}{3}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{3}\times \frac{3}{10}=\frac{x+\frac{2}{3}}{\frac{8}{3}}$$

Multiply \frac{1}{3} and \frac{3}{10} to get \frac{1}{10}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{10}=\frac{x+\frac{2}{3}}{\frac{8}{3}}$$

Divide each term of x+\frac{2}{3} by \frac{8}{3} to get \frac{x}{\frac{8}{3}}+\frac{\frac{2}{3}}{\frac{8}{3}}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{10}=\frac{x}{\frac{8}{3}}+\frac{\frac{2}{3}}{\frac{8}{3}}$$

Divide \frac{2}{3} by \frac{8}{3} by multiplying \frac{2}{3} by the reciprocal of \frac{8}{3}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{10}=\frac{x}{\frac{8}{3}}+\frac{2}{3}\times \frac{3}{8}$$

Multiply \frac{2}{3} and \frac{3}{8} to get \frac{1}{4}.

$$\frac{y}{\frac{10}{3}}+\frac{1}{10}=\frac{x}{\frac{8}{3}}+\frac{1}{4}$$

Subtract \frac{1}{10} from both sides.

$$\frac{y}{\frac{10}{3}}=\frac{x}{\frac{8}{3}}+\frac{1}{4}-\frac{1}{10}$$

Subtract \frac{1}{10} from \frac{1}{4} to get \frac{3}{20}.

$$\frac{y}{\frac{10}{3}}=\frac{x}{\frac{8}{3}}+\frac{3}{20}$$

The equation is in standard form.

$$\frac{3}{10}y=\frac{3x}{8}+\frac{3}{20}$$

Divide both sides of the equation by \frac{3}{10}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{10}y}{\frac{3}{10}}=\frac{\frac{3x}{8}+\frac{3}{20}}{\frac{3}{10}}$$

Dividing by \frac{3}{10} undoes the multiplication by \frac{3}{10}.

$$y=\frac{\frac{3x}{8}+\frac{3}{20}}{\frac{3}{10}}$$

Divide \frac{3x}{8}+\frac{3}{20} by \frac{3}{10} by multiplying \frac{3x}{8}+\frac{3}{20} by the reciprocal of \frac{3}{10}.

$$y=\frac{5x}{4}+\frac{1}{2}$$