Solve operatorname{gen}20x+40y=400

$$\operatorname { gen } 20 x + 40 y = 400$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=-\frac{40\left(y-10\right)}{en_{20}x}\text{, }&x\neq 0\text{ and }n_{20}\neq 0\\g\in \mathrm{C}\text{, }&\left(n_{20}=0\text{ or }x=0\right)\text{ and }y=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 40y from both sides.

$$gen_{20}x=400-40y$$

The equation is in standard form.

$$en_{20}xg=400-40y$$

Divide both sides by en_{20}x.

$$\frac{en_{20}xg}{en_{20}x}=\frac{400-40y}{en_{20}x}$$

Dividing by en_{20}x undoes the multiplication by en_{20}x.

$$g=\frac{400-40y}{en_{20}x}$$

Divide 400-40y by en_{20}x.

$$g=\frac{40\left(10-y\right)}{en_{20}x}$$

Solve for n_20 (complex solution)

$$\left\{\begin{matrix}n_{20}=-\frac{40\left(y-10\right)}{egx}\text{, }&x\neq 0\text{ and }g\neq 0\\n_{20}\in \mathrm{C}\text{, }&\left(x=0\text{ or }g=0\right)\text{ and }y=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 40y from both sides.

$$gen_{20}x=400-40y$$

The equation is in standard form.

$$egxn_{20}=400-40y$$

Divide both sides by gex.

$$\frac{egxn_{20}}{egx}=\frac{400-40y}{egx}$$

Dividing by gex undoes the multiplication by gex.

$$n_{20}=\frac{400-40y}{egx}$$

Divide 400-40y by gex.

$$n_{20}=\frac{40\left(10-y\right)}{egx}$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{40\left(y-10\right)}{en_{20}x}\text{, }&x\neq 0\text{ and }n_{20}\neq 0\\g\in \mathrm{R}\text{, }&\left(n_{20}=0\text{ or }x=0\right)\text{ and }y=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 40y from both sides.

$$gen_{20}x=400-40y$$

The equation is in standard form.

$$en_{20}xg=400-40y$$

Divide both sides by en_{20}x.

$$\frac{en_{20}xg}{en_{20}x}=\frac{400-40y}{en_{20}x}$$

Dividing by en_{20}x undoes the multiplication by en_{20}x.

$$g=\frac{400-40y}{en_{20}x}$$

Divide 400-40y by en_{20}x.

$$g=\frac{40\left(10-y\right)}{en_{20}x}$$

Solve for n_20

$$\left\{\begin{matrix}n_{20}=-\frac{40\left(y-10\right)}{egx}\text{, }&x\neq 0\text{ and }g\neq 0\\n_{20}\in \mathrm{R}\text{, }&\left(x=0\text{ or }g=0\right)\text{ and }y=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 40y from both sides.

$$gen_{20}x=400-40y$$

The equation is in standard form.

$$egxn_{20}=400-40y$$

Divide both sides by gex.

$$\frac{egxn_{20}}{egx}=\frac{400-40y}{egx}$$

Dividing by gex undoes the multiplication by gex.

$$n_{20}=\frac{400-40y}{egx}$$

Divide 400-40y by gex.

$$n_{20}=\frac{40\left(10-y\right)}{egx}$$