Solve x^2+y^2-2x-8y+17=x^2+y^2+2x-4y+5

$$x ^ { 2 } + y ^ { 2 } - 2 x - 8 y + 17 = x ^ { 2 } + y ^ { 2 } + 2 x - 4 y + 5$$

Solve for x

$$x=3-y$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$x^{2}+y^{2}-2x-8y+17-x^{2}=y^{2}+2x-4y+5$$

Combine x^{2} and -x^{2} to get 0.

$$y^{2}-2x-8y+17=y^{2}+2x-4y+5$$

Subtract 2x from both sides.

$$y^{2}-2x-8y+17-2x=y^{2}-4y+5$$

Combine -2x and -2x to get -4x.

$$y^{2}-4x-8y+17=y^{2}-4y+5$$

Subtract y^{2} from both sides.

$$-4x-8y+17=y^{2}-4y+5-y^{2}$$

Combine y^{2} and -y^{2} to get 0.

$$-4x-8y+17=-4y+5$$

Add 8y to both sides.

$$-4x+17=-4y+5+8y$$

Combine -4y and 8y to get 4y.

$$-4x+17=4y+5$$

Subtract 17 from both sides.

$$-4x=4y+5-17$$

Subtract 17 from 5 to get -12.

$$-4x=4y-12$$

Divide both sides by -4.

$$\frac{-4x}{-4}=\frac{4y-12}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x=\frac{4y-12}{-4}$$

Divide -12+4y by -4.

$$x=3-y$$

Solve for y

$$y=3-x$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$x^{2}+y^{2}-2x-8y+17-y^{2}=x^{2}+2x-4y+5$$

Combine y^{2} and -y^{2} to get 0.

$$x^{2}-2x-8y+17=x^{2}+2x-4y+5$$

Add 4y to both sides.

$$x^{2}-2x-8y+17+4y=x^{2}+2x+5$$

Combine -8y and 4y to get -4y.

$$x^{2}-2x-4y+17=x^{2}+2x+5$$

Subtract x^{2} from both sides.

$$-2x-4y+17=x^{2}+2x+5-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-2x-4y+17=2x+5$$

Add 2x to both sides.

$$-4y+17=2x+5+2x$$

Combine 2x and 2x to get 4x.

$$-4y+17=4x+5$$

Subtract 17 from both sides.

$$-4y=4x+5-17$$

Subtract 17 from 5 to get -12.

$$-4y=4x-12$$

Divide both sides by -4.

$$\frac{-4y}{-4}=\frac{4x-12}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$y=\frac{4x-12}{-4}$$

Divide -12+4x by -4.

$$y=3-x$$