Solve bx+ay=11x

$$b x + a y = 11 x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x\left(b-11\right)}{y}\text{, }&y\neq 0\\a\in \mathrm{C}\text{, }&\left(b=11\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ay=11x-bx$$

The equation is in standard form.

$$ya=11x-bx$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{x\left(11-b\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{x\left(11-b\right)}{y}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{ay}{x}+11\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&\left(a=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ay from both sides.

$$bx=11x-ay$$

The equation is in standard form.

$$xb=11x-ay$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{11x-ay}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{11x-ay}{x}$$

Divide 11x-ay by x.

$$b=-\frac{ay}{x}+11$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{x\left(b-11\right)}{y}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&\left(b=11\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ay=11x-bx$$

The equation is in standard form.

$$ya=11x-bx$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{x\left(11-b\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{x\left(11-b\right)}{y}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ay}{x}+11\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&\left(a=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ay from both sides.

$$bx=11x-ay$$

The equation is in standard form.

$$xb=11x-ay$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{11x-ay}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{11x-ay}{x}$$

Divide 11x-ay by x.

$$b=-\frac{ay}{x}+11$$