Solve y=ax+b/cx+d

$$y = \frac { a x + b } { c x + d }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{cxy+dy-b}{x}\text{, }&x\neq 0\text{ and }d\neq -cx\\a\in \mathrm{C}\text{, }&b=dy\text{ and }x=0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by cx+d.

$$y\left(cx+d\right)=ax+b$$

Use the distributive property to multiply y by cx+d.

$$ycx+yd=ax+b$$

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

$$ax+b=ycx+yd$$

Subtract b from both sides.

$$ax=ycx+yd-b$$

The equation is in standard form.

$$xa=cxy+dy-b$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{cxy+dy-b}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{cxy+dy-b}{x}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{cxy+dy-b}{x}\text{, }&x\neq 0\text{ and }d\neq -cx\\a\in \mathrm{R}\text{, }&b=dy\text{ and }x=0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by cx+d.

$$y\left(cx+d\right)=ax+b$$

Use the distributive property to multiply y by cx+d.

$$ycx+yd=ax+b$$

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

$$ax+b=ycx+yd$$

Subtract b from both sides.

$$ax=ycx+yd-b$$

The equation is in standard form.

$$xa=cxy+dy-b$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{cxy+dy-b}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{cxy+dy-b}{x}$$

Solve for b

$$b=cxy-ax+dy$$

$$d\neq -cx$$