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

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

Solve for x

$$x=19-7y$$

Steps for Solving Linear Equation

Subtract 2 from 3 to get 1.

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

Anything divided by one gives itself.

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

Subtract 5 from -2 to get -7.

$$y-2=\frac{x-5}{-7}$$

Multiply both numerator and denominator by -1.

$$y-2=\frac{-x+5}{7}$$

Divide each term of -x+5 by 7 to get -\frac{1}{7}x+\frac{5}{7}.

$$y-2=-\frac{1}{7}x+\frac{5}{7}$$

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

$$-\frac{1}{7}x+\frac{5}{7}=y-2$$

Subtract \frac{5}{7} from both sides.

$$-\frac{1}{7}x=y-2-\frac{5}{7}$$

Subtract \frac{5}{7} from -2 to get -\frac{19}{7}.

$$-\frac{1}{7}x=y-\frac{19}{7}$$

Multiply both sides by -7.

$$\frac{-\frac{1}{7}x}{-\frac{1}{7}}=\frac{y-\frac{19}{7}}{-\frac{1}{7}}$$

Dividing by -\frac{1}{7} undoes the multiplication by -\frac{1}{7}.

$$x=\frac{y-\frac{19}{7}}{-\frac{1}{7}}$$

Divide y-\frac{19}{7} by -\frac{1}{7} by multiplying y-\frac{19}{7} by the reciprocal of -\frac{1}{7}.

$$x=19-7y$$

Solve for y

$$y=\frac{19-x}{7}$$

Solution Steps

Subtract 2 from 3 to get 1.

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

Anything divided by one gives itself.

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

Subtract 5 from -2 to get -7.

$$y-2=\frac{x-5}{-7}$$

Multiply both numerator and denominator by -1.

$$y-2=\frac{-x+5}{7}$$

Divide each term of -x+5 by 7 to get -\frac{1}{7}x+\frac{5}{7}.

$$y-2=-\frac{1}{7}x+\frac{5}{7}$$

Add 2 to both sides.

$$y=-\frac{1}{7}x+\frac{5}{7}+2$$

Add \frac{5}{7} and 2 to get \frac{19}{7}.

$$y=-\frac{1}{7}x+\frac{19}{7}$$