Solve x-(3+k)y-3=0

$$x - ( 3 + k ) y - 3 = 0$$

Solve for k (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply 3+k by y.

$$x-\left(3y+ky\right)-3=0$$

To find the opposite of 3y+ky, find the opposite of each term.

$$x-3y-ky-3=0$$

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

$$-3y-ky-3=-x$$

Add 3y to both sides.

$$-ky-3=-x+3y$$

Add 3 to both sides.

$$-ky=-x+3y+3$$

The equation is in standard form.

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

Divide both sides by -y.

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

Dividing by -y undoes the multiplication by -y.

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

Divide 3y-x+3 by -y.

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

Solve for k

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

Steps for Solving Linear Equation

Use the distributive property to multiply 3+k by y.

$$x-\left(3y+ky\right)-3=0$$

To find the opposite of 3y+ky, find the opposite of each term.

$$x-3y-ky-3=0$$

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

$$-3y-ky-3=-x$$

Add 3y to both sides.

$$-ky-3=-x+3y$$

Add 3 to both sides.

$$-ky=-x+3y+3$$

The equation is in standard form.

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

Divide both sides by -y.

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

Dividing by -y undoes the multiplication by -y.

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

Divide 3y-x+3 by -y.

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

Solve for x

$$x=ky+3y+3$$

Solution Steps

Use the distributive property to multiply 3+k by y.

$$x-\left(3y+ky\right)-3=0$$

To find the opposite of 3y+ky, find the opposite of each term.

$$x-3y-ky-3=0$$

Add 3y to both sides. Anything plus zero gives itself.

$$x-ky-3=3y$$

Add ky to both sides.

$$x-3=3y+ky$$

Add 3 to both sides.

$$x=3y+ky+3$$