Solve x+ky=3k/2

$$x+ky = \frac{ 3k }{ 2 }$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{2x}{2y-3}\text{, }&y\neq \frac{3}{2}\\k\in \mathrm{C}\text{, }&x=0\text{ and }y=\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x+2ky=3k$$

Subtract 3k from both sides.

$$2x+2ky-3k=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$2ky-3k=-2x$$

Combine all terms containing k.

$$\left(2y-3\right)k=-2x$$

Divide both sides by 2y-3.

$$\frac{\left(2y-3\right)k}{2y-3}=-\frac{2x}{2y-3}$$

Dividing by 2y-3 undoes the multiplication by 2y-3.

$$k=-\frac{2x}{2y-3}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{2x}{2y-3}\text{, }&y\neq \frac{3}{2}\\k\in \mathrm{R}\text{, }&x=0\text{ and }y=\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x+2ky=3k$$

Subtract 3k from both sides.

$$2x+2ky-3k=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$2ky-3k=-2x$$

Combine all terms containing k.

$$\left(2y-3\right)k=-2x$$

Divide both sides by 2y-3.

$$\frac{\left(2y-3\right)k}{2y-3}=-\frac{2x}{2y-3}$$

Dividing by 2y-3 undoes the multiplication by 2y-3.

$$k=-\frac{2x}{2y-3}$$

Solve for x

$$x=\frac{k\left(3-2y\right)}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x+2ky=3k$$

Subtract 2ky from both sides.

$$2x=3k-2ky$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{k\left(3-2y\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{k\left(3-2y\right)}{2}$$

Divide k\left(3-2y\right) by 2.

$$x=-ky+\frac{3k}{2}$$