Solve y-3/5-3=x-2/-3-2

$$\frac { y - 3 } { 5 - 3 } = \frac { x - 2 } { - 3 - 2 }$$

Solve for x

$$x=\frac{19-5y}{2}$$

Steps for Solving Linear Equation

Subtract 3 from 5 to get 2.

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

Subtract 2 from -3 to get -5.

$$\frac{y-3}{2}=\frac{x-2}{-5}$$

Multiply both numerator and denominator by -1.

$$\frac{y-3}{2}=\frac{-x+2}{5}$$

Divide each term of y-3 by 2 to get \frac{1}{2}y-\frac{3}{2}.

$$\frac{1}{2}y-\frac{3}{2}=\frac{-x+2}{5}$$

Divide each term of -x+2 by 5 to get -\frac{1}{5}x+\frac{2}{5}.

$$\frac{1}{2}y-\frac{3}{2}=-\frac{1}{5}x+\frac{2}{5}$$

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

$$-\frac{1}{5}x+\frac{2}{5}=\frac{1}{2}y-\frac{3}{2}$$

Subtract \frac{2}{5} from both sides.

$$-\frac{1}{5}x=\frac{1}{2}y-\frac{3}{2}-\frac{2}{5}$$

Subtract \frac{2}{5} from -\frac{3}{2} to get -\frac{19}{10}.

$$-\frac{1}{5}x=\frac{1}{2}y-\frac{19}{10}$$

The equation is in standard form.

$$-\frac{1}{5}x=\frac{y}{2}-\frac{19}{10}$$

Multiply both sides by -5.

$$\frac{-\frac{1}{5}x}{-\frac{1}{5}}=\frac{\frac{y}{2}-\frac{19}{10}}{-\frac{1}{5}}$$

Dividing by -\frac{1}{5} undoes the multiplication by -\frac{1}{5}.

$$x=\frac{\frac{y}{2}-\frac{19}{10}}{-\frac{1}{5}}$$

Divide \frac{y}{2}-\frac{19}{10} by -\frac{1}{5} by multiplying \frac{y}{2}-\frac{19}{10} by the reciprocal of -\frac{1}{5}.

$$x=\frac{19-5y}{2}$$

Solve for y

$$y=\frac{19-2x}{5}$$

Steps for Solving Linear Equation

Subtract 3 from 5 to get 2.

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

Subtract 2 from -3 to get -5.

$$\frac{y-3}{2}=\frac{x-2}{-5}$$

Multiply both numerator and denominator by -1.

$$\frac{y-3}{2}=\frac{-x+2}{5}$$

Divide each term of y-3 by 2 to get \frac{1}{2}y-\frac{3}{2}.

$$\frac{1}{2}y-\frac{3}{2}=\frac{-x+2}{5}$$

Divide each term of -x+2 by 5 to get -\frac{1}{5}x+\frac{2}{5}.

$$\frac{1}{2}y-\frac{3}{2}=-\frac{1}{5}x+\frac{2}{5}$$

Add \frac{3}{2} to both sides.

$$\frac{1}{2}y=-\frac{1}{5}x+\frac{2}{5}+\frac{3}{2}$$

Add \frac{2}{5} and \frac{3}{2} to get \frac{19}{10}.

$$\frac{1}{2}y=-\frac{1}{5}x+\frac{19}{10}$$

The equation is in standard form.

$$\frac{1}{2}y=-\frac{x}{5}+\frac{19}{10}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}y}{\frac{1}{2}}=\frac{-\frac{x}{5}+\frac{19}{10}}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$y=\frac{-\frac{x}{5}+\frac{19}{10}}{\frac{1}{2}}$$

Divide -\frac{x}{5}+\frac{19}{10} by \frac{1}{2} by multiplying -\frac{x}{5}+\frac{19}{10} by the reciprocal of \frac{1}{2}.

$$y=\frac{19-2x}{5}$$