Solve x2+y2-4x+4y-6=0

$$x2+y2-4x+4y-6=0$$

Solve for x

$$x=\frac{x_{2}+4y+y_{2}-6}{4}$$

Steps for Solving Linear Equation

Subtract x_{2} from both sides. Anything subtracted from zero gives its negation.

$$y_{2}-4x+4y-6=-x_{2}$$

Subtract y_{2} from both sides.

$$-4x+4y-6=-x_{2}-y_{2}$$

Subtract 4y from both sides.

$$-4x-6=-x_{2}-y_{2}-4y$$

Add 6 to both sides.

$$-4x=-x_{2}-y_{2}-4y+6$$

The equation is in standard form.

$$-4x=6-y_{2}-4y-x_{2}$$

Divide both sides by -4.

$$\frac{-4x}{-4}=\frac{6-y_{2}-4y-x_{2}}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x=\frac{6-y_{2}-4y-x_{2}}{-4}$$

Divide -x_{2}-y_{2}-4y+6 by -4.

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

Solve for x_2

$$x_{2}=4x-4y-y_{2}+6$$

Solution Steps

Subtract y_{2} from both sides. Anything subtracted from zero gives its negation.

$$x_{2}-4x+4y-6=-y_{2}$$

Add 4x to both sides.

$$x_{2}+4y-6=-y_{2}+4x$$

Subtract 4y from both sides.

$$x_{2}-6=-y_{2}+4x-4y$$

Add 6 to both sides.

$$x_{2}=-y_{2}+4x-4y+6$$