Solve 6x^2+6y^2=6(x^2+y^2)

$$6 x ^ { 2 } + 6 y ^ { 2 } = 6 ( x ^ { 2 } + y ^ { 2 } )$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 6 by x^{2}+y^{2}.

$$6x^{2}+6y^{2}=6x^{2}+6y^{2}$$

Subtract 6x^{2} from both sides.

$$6x^{2}+6y^{2}-6x^{2}=6y^{2}$$

Combine 6x^{2} and -6x^{2} to get 0.

$$6y^{2}=6y^{2}$$

Cancel out 6 on both sides.

$$y^{2}=y^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for y (complex solution)

$$y\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 6 by x^{2}+y^{2}.

$$6x^{2}+6y^{2}=6x^{2}+6y^{2}$$

Subtract 6y^{2} from both sides.

$$6x^{2}+6y^{2}-6y^{2}=6x^{2}$$

Combine 6y^{2} and -6y^{2} to get 0.

$$6x^{2}=6x^{2}$$

Cancel out 6 on both sides.

$$x^{2}=x^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 6 by x^{2}+y^{2}.

$$6x^{2}+6y^{2}=6x^{2}+6y^{2}$$

Subtract 6x^{2} from both sides.

$$6x^{2}+6y^{2}-6x^{2}=6y^{2}$$

Combine 6x^{2} and -6x^{2} to get 0.

$$6y^{2}=6y^{2}$$

Cancel out 6 on both sides.

$$y^{2}=y^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Solve for y

$$y\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 6 by x^{2}+y^{2}.

$$6x^{2}+6y^{2}=6x^{2}+6y^{2}$$

Subtract 6y^{2} from both sides.

$$6x^{2}+6y^{2}-6y^{2}=6x^{2}$$

Combine 6y^{2} and -6y^{2} to get 0.

$$6x^{2}=6x^{2}$$

Cancel out 6 on both sides.

$$x^{2}=x^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{R}$$