Solve y-(-5)/(-7)-(-5)=x-(-2)/3-(-2)

$$\frac{ y-(-5) }{ (-7)-(-5) } = \frac{ x-(-2) }{ 3-(-2) }$$

Solve for x

$$x=\frac{-5y-29}{2}$$

Steps for Solving Linear Equation

The opposite of -5 is 5.

$$\frac{y+5}{-7-\left(-5\right)}=\frac{x-\left(-2\right)}{3-\left(-2\right)}$$

The opposite of -5 is 5.

$$\frac{y+5}{-7+5}=\frac{x-\left(-2\right)}{3-\left(-2\right)}$$

Add -7 and 5 to get -2.

$$\frac{y+5}{-2}=\frac{x-\left(-2\right)}{3-\left(-2\right)}$$

Multiply both numerator and denominator by -1.

$$\frac{-y-5}{2}=\frac{x-\left(-2\right)}{3-\left(-2\right)}$$

The opposite of -2 is 2.

$$\frac{-y-5}{2}=\frac{x+2}{3-\left(-2\right)}$$

The opposite of -2 is 2.

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

Add 3 and 2 to get 5.

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

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

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

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

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

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

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

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

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

Subtract \frac{2}{5} from -\frac{5}{2} to get -\frac{29}{10}.

$$\frac{1}{5}x=-\frac{1}{2}y-\frac{29}{10}$$

The equation is in standard form.

$$\frac{1}{5}x=-\frac{y}{2}-\frac{29}{10}$$

Multiply both sides by 5.

$$\frac{\frac{1}{5}x}{\frac{1}{5}}=\frac{-\frac{y}{2}-\frac{29}{10}}{\frac{1}{5}}$$

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

$$x=\frac{-\frac{y}{2}-\frac{29}{10}}{\frac{1}{5}}$$

Divide -\frac{y}{2}-\frac{29}{10} by \frac{1}{5} by multiplying -\frac{y}{2}-\frac{29}{10} by the reciprocal of \frac{1}{5}.

$$x=\frac{-5y-29}{2}$$

Solve for y

$$y=\frac{-2x-29}{5}$$

Steps for Solving Linear Equation

The opposite of -5 is 5.

$$\frac{y+5}{-7-\left(-5\right)}=\frac{x-\left(-2\right)}{3-\left(-2\right)}$$

The opposite of -5 is 5.

$$\frac{y+5}{-7+5}=\frac{x-\left(-2\right)}{3-\left(-2\right)}$$

Add -7 and 5 to get -2.

$$\frac{y+5}{-2}=\frac{x-\left(-2\right)}{3-\left(-2\right)}$$

Multiply both numerator and denominator by -1.

$$\frac{-y-5}{2}=\frac{x-\left(-2\right)}{3-\left(-2\right)}$$

The opposite of -2 is 2.

$$\frac{-y-5}{2}=\frac{x+2}{3-\left(-2\right)}$$

The opposite of -2 is 2.

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

Add 3 and 2 to get 5.

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

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

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

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

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

Add \frac{5}{2} to both sides.

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

Add \frac{2}{5} and \frac{5}{2} to get \frac{29}{10}.

$$-\frac{1}{2}y=\frac{1}{5}x+\frac{29}{10}$$

The equation is in standard form.

$$-\frac{1}{2}y=\frac{x}{5}+\frac{29}{10}$$

Multiply both sides by -2.

$$\frac{-\frac{1}{2}y}{-\frac{1}{2}}=\frac{\frac{x}{5}+\frac{29}{10}}{-\frac{1}{2}}$$

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

$$y=\frac{\frac{x}{5}+\frac{29}{10}}{-\frac{1}{2}}$$

Divide \frac{x}{5}+\frac{29}{10} by -\frac{1}{2} by multiplying \frac{x}{5}+\frac{29}{10} by the reciprocal of -\frac{1}{2}.

$$y=\frac{-2x-29}{5}$$