Solve =x^{6}yquad(C)(-x^{2})x^2=-x^5quad(D)(-x^2)x^2=

$$= x ^ { 6 } y \quad ( C ) ( - x ^ { 2 } ) x ^ { 2 } = - x ^ { 5 } \quad ( D ) ( - x ^ { 2 } ) x ^ { 2 } =$$

Solve for C (complex solution)

$$\left\{\begin{matrix}C=-\frac{D}{xy}\text{, }&x\neq 0\text{ and }y\neq 0\\C\in \mathrm{C}\text{, }&\left(D=0\text{ and }y=0\right)\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$x^{8}yC\left(-x^{2}\right)=\left(-x^{5}\right)D\left(-x^{2}\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$x^{10}yC\left(-1\right)=-x^{5}D\left(-1\right)x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$x^{10}yC\left(-1\right)=-x^{7}D\left(-1\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$x^{10}yC\left(-1\right)=-x^{9}D\left(-1\right)$$

Multiply -1 and -1 to get 1.

$$x^{10}yC\left(-1\right)=x^{9}D$$

The equation is in standard form.

$$\left(-yx^{10}\right)C=Dx^{9}$$

Divide both sides by -x^{10}y.

$$\frac{\left(-yx^{10}\right)C}{-yx^{10}}=\frac{Dx^{9}}{-yx^{10}}$$

Dividing by -x^{10}y undoes the multiplication by -x^{10}y.

$$C=\frac{Dx^{9}}{-yx^{10}}$$

Divide x^{9}D by -x^{10}y.

$$C=-\frac{D}{xy}$$

Solve for D (complex solution)

$$\left\{\begin{matrix}\\D=-Cxy\text{, }&\text{unconditionally}\\D\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$x^{8}yC\left(-x^{2}\right)=\left(-x^{5}\right)D\left(-x^{2}\right)x^{2}$$

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

$$\left(-x^{5}\right)D\left(-x^{2}\right)x^{2}=x^{8}yC\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$x^{5}Dx^{2}x^{2}=x^{8}yC\left(-1\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$x^{7}Dx^{2}=x^{8}yC\left(-1\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$x^{9}D=x^{8}yC\left(-1\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$x^{9}D=x^{10}yC\left(-1\right)$$

The equation is in standard form.

$$x^{9}D=-Cyx^{10}$$

Divide both sides by x^{9}.

$$\frac{x^{9}D}{x^{9}}=-\frac{Cyx^{10}}{x^{9}}$$

Dividing by x^{9} undoes the multiplication by x^{9}.

$$D=-\frac{Cyx^{10}}{x^{9}}$$

Divide -x^{10}yC by x^{9}.

$$D=-Cxy$$

Solve for C

$$\left\{\begin{matrix}C=-\frac{D}{xy}\text{, }&x\neq 0\text{ and }y\neq 0\\C\in \mathrm{R}\text{, }&\left(D=0\text{ and }y=0\right)\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$x^{8}yC\left(-x^{2}\right)=\left(-x^{5}\right)D\left(-x^{2}\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$x^{10}yC\left(-1\right)=-x^{5}D\left(-1\right)x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$x^{10}yC\left(-1\right)=-x^{7}D\left(-1\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$x^{10}yC\left(-1\right)=-x^{9}D\left(-1\right)$$

Multiply -1 and -1 to get 1.

$$x^{10}yC\left(-1\right)=x^{9}D$$

The equation is in standard form.

$$\left(-yx^{10}\right)C=Dx^{9}$$

Divide both sides by -x^{10}y.

$$\frac{\left(-yx^{10}\right)C}{-yx^{10}}=\frac{Dx^{9}}{-yx^{10}}$$

Dividing by -x^{10}y undoes the multiplication by -x^{10}y.

$$C=\frac{Dx^{9}}{-yx^{10}}$$

Divide x^{9}D by -x^{10}y.

$$C=-\frac{D}{xy}$$

Solve for D

$$\left\{\begin{matrix}\\D=-Cxy\text{, }&\text{unconditionally}\\D\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$x^{8}yC\left(-x^{2}\right)=\left(-x^{5}\right)D\left(-x^{2}\right)x^{2}$$

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

$$\left(-x^{5}\right)D\left(-x^{2}\right)x^{2}=x^{8}yC\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$x^{5}Dx^{2}x^{2}=x^{8}yC\left(-1\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$x^{7}Dx^{2}=x^{8}yC\left(-1\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$x^{9}D=x^{8}yC\left(-1\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$x^{9}D=x^{10}yC\left(-1\right)$$

The equation is in standard form.

$$x^{9}D=-Cyx^{10}$$

Divide both sides by x^{9}.

$$\frac{x^{9}D}{x^{9}}=-\frac{Cyx^{10}}{x^{9}}$$

Dividing by x^{9} undoes the multiplication by x^{9}.

$$D=-\frac{Cyx^{10}}{x^{9}}$$

Divide -x^{10}yC by x^{9}.

$$D=-Cxy$$