Solve x-2/frac{4{3}-2}=y+4/frac{2{3}+4}

$$\frac { x - 2 } { \frac { 4 } { 3 } - 2 } = \frac { y + 4 } { \frac { 2 } { 3 } + 4 }$$

Solve for x

$$x=\frac{10-y}{7}$$

Steps for Solving Linear Equation

Subtract 2 from \frac{4}{3} to get -\frac{2}{3}.

$$\frac{x-2}{-\frac{2}{3}}=\frac{y+4}{\frac{2}{3}+4}$$

Multiply both numerator and denominator by -1.

$$\frac{-x+2}{\frac{2}{3}}=\frac{y+4}{\frac{2}{3}+4}$$

Add \frac{2}{3} and 4 to get \frac{14}{3}.

$$\frac{-x+2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

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

$$\frac{-x}{\frac{2}{3}}+\frac{2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

Divide -x by \frac{2}{3} to get -\frac{3}{2}x.

$$-\frac{3}{2}x+\frac{2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

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

$$-\frac{3}{2}x+2\times \frac{3}{2}=\frac{y+4}{\frac{14}{3}}$$

Multiply 2 and \frac{3}{2} to get 3.

$$-\frac{3}{2}x+3=\frac{y+4}{\frac{14}{3}}$$

Divide each term of y+4 by \frac{14}{3} to get \frac{y}{\frac{14}{3}}+\frac{4}{\frac{14}{3}}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+\frac{4}{\frac{14}{3}}$$

Divide 4 by \frac{14}{3} by multiplying 4 by the reciprocal of \frac{14}{3}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+4\times \frac{3}{14}$$

Multiply 4 and \frac{3}{14} to get \frac{6}{7}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+\frac{6}{7}$$

Subtract 3 from both sides.

$$-\frac{3}{2}x=\frac{y}{\frac{14}{3}}+\frac{6}{7}-3$$

Subtract 3 from \frac{6}{7} to get -\frac{15}{7}.

$$-\frac{3}{2}x=\frac{y}{\frac{14}{3}}-\frac{15}{7}$$

The equation is in standard form.

$$-\frac{3}{2}x=\frac{3y}{14}-\frac{15}{7}$$

Divide both sides of the equation by -\frac{3}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{3}{2}x}{-\frac{3}{2}}=\frac{\frac{3y}{14}-\frac{15}{7}}{-\frac{3}{2}}$$

Dividing by -\frac{3}{2} undoes the multiplication by -\frac{3}{2}.

$$x=\frac{\frac{3y}{14}-\frac{15}{7}}{-\frac{3}{2}}$$

Divide -\frac{15}{7}+\frac{3y}{14} by -\frac{3}{2} by multiplying -\frac{15}{7}+\frac{3y}{14} by the reciprocal of -\frac{3}{2}.

$$x=\frac{10-y}{7}$$

Solve for y

$$y=10-7x$$

Steps for Solving Linear Equation

Subtract 2 from \frac{4}{3} to get -\frac{2}{3}.

$$\frac{x-2}{-\frac{2}{3}}=\frac{y+4}{\frac{2}{3}+4}$$

Multiply both numerator and denominator by -1.

$$\frac{-x+2}{\frac{2}{3}}=\frac{y+4}{\frac{2}{3}+4}$$

Add \frac{2}{3} and 4 to get \frac{14}{3}.

$$\frac{-x+2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

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

$$\frac{-x}{\frac{2}{3}}+\frac{2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

Divide -x by \frac{2}{3} to get -\frac{3}{2}x.

$$-\frac{3}{2}x+\frac{2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

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

$$-\frac{3}{2}x+2\times \frac{3}{2}=\frac{y+4}{\frac{14}{3}}$$

Multiply 2 and \frac{3}{2} to get 3.

$$-\frac{3}{2}x+3=\frac{y+4}{\frac{14}{3}}$$

Divide each term of y+4 by \frac{14}{3} to get \frac{y}{\frac{14}{3}}+\frac{4}{\frac{14}{3}}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+\frac{4}{\frac{14}{3}}$$

Divide 4 by \frac{14}{3} by multiplying 4 by the reciprocal of \frac{14}{3}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+4\times \frac{3}{14}$$

Multiply 4 and \frac{3}{14} to get \frac{6}{7}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+\frac{6}{7}$$

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

$$\frac{y}{\frac{14}{3}}+\frac{6}{7}=-\frac{3}{2}x+3$$

Subtract \frac{6}{7} from both sides.

$$\frac{y}{\frac{14}{3}}=-\frac{3}{2}x+3-\frac{6}{7}$$

Subtract \frac{6}{7} from 3 to get \frac{15}{7}.

$$\frac{y}{\frac{14}{3}}=-\frac{3}{2}x+\frac{15}{7}$$

The equation is in standard form.

$$\frac{3}{14}y=-\frac{3x}{2}+\frac{15}{7}$$

Divide both sides of the equation by \frac{3}{14}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{14}y}{\frac{3}{14}}=\frac{-\frac{3x}{2}+\frac{15}{7}}{\frac{3}{14}}$$

Dividing by \frac{3}{14} undoes the multiplication by \frac{3}{14}.

$$y=\frac{-\frac{3x}{2}+\frac{15}{7}}{\frac{3}{14}}$$

Divide -\frac{3x}{2}+\frac{15}{7} by \frac{3}{14} by multiplying -\frac{3x}{2}+\frac{15}{7} by the reciprocal of \frac{3}{14}.

$$y=10-7x$$