Solve x^2+y^2-10x-12y+47=x^2+y^2-2x-6y+1

$$x ^ { 2 } + y ^ { 2 } - 10 x - 12 y + 47 = x ^ { 2 } + y ^ { 2 } - 2 x - 6 y + 1$$

Solve for x

$$x=\frac{23-3y}{4}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$x^{2}+y^{2}-10x-12y+47-x^{2}=y^{2}-2x-6y+1$$

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

$$y^{2}-10x-12y+47=y^{2}-2x-6y+1$$

Add 2x to both sides.

$$y^{2}-10x-12y+47+2x=y^{2}-6y+1$$

Combine -10x and 2x to get -8x.

$$y^{2}-8x-12y+47=y^{2}-6y+1$$

Subtract y^{2} from both sides.

$$-8x-12y+47=y^{2}-6y+1-y^{2}$$

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

$$-8x-12y+47=-6y+1$$

Add 12y to both sides.

$$-8x+47=-6y+1+12y$$

Combine -6y and 12y to get 6y.

$$-8x+47=6y+1$$

Subtract 47 from both sides.

$$-8x=6y+1-47$$

Subtract 47 from 1 to get -46.

$$-8x=6y-46$$

Divide both sides by -8.

$$\frac{-8x}{-8}=\frac{6y-46}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x=\frac{6y-46}{-8}$$

Divide 6y-46 by -8.

$$x=\frac{23-3y}{4}$$

Solve for y

$$y=\frac{23-4x}{3}$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$x^{2}+y^{2}-10x-12y+47-y^{2}=x^{2}-2x-6y+1$$

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

$$x^{2}-10x-12y+47=x^{2}-2x-6y+1$$

Add 6y to both sides.

$$x^{2}-10x-12y+47+6y=x^{2}-2x+1$$

Combine -12y and 6y to get -6y.

$$x^{2}-10x-6y+47=x^{2}-2x+1$$

Subtract x^{2} from both sides.

$$-10x-6y+47=x^{2}-2x+1-x^{2}$$

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

$$-10x-6y+47=-2x+1$$

Add 10x to both sides.

$$-6y+47=-2x+1+10x$$

Combine -2x and 10x to get 8x.

$$-6y+47=8x+1$$

Subtract 47 from both sides.

$$-6y=8x+1-47$$

Subtract 47 from 1 to get -46.

$$-6y=8x-46$$

Divide both sides by -6.

$$\frac{-6y}{-6}=\frac{8x-46}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$y=\frac{8x-46}{-6}$$

Divide 8x-46 by -6.

$$y=\frac{23-4x}{3}$$