Solve k-y+4=x+ky-3

$$k - y + 4 = x + k y - 3$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{7-y-x}{1-y}\text{, }&y\neq 1\\k\in \mathrm{C}\text{, }&y=1\text{ and }x=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ky from both sides.

$$k-y+4-ky=x-3$$

Add y to both sides.

$$k+4-ky=x-3+y$$

Subtract 4 from both sides.

$$k-ky=x-3+y-4$$

Subtract 4 from -3 to get -7.

$$k-ky=x-7+y$$

Combine all terms containing k.

$$\left(1-y\right)k=x-7+y$$

The equation is in standard form.

$$\left(1-y\right)k=x+y-7$$

Divide both sides by 1-y.

$$\frac{\left(1-y\right)k}{1-y}=\frac{x+y-7}{1-y}$$

Dividing by 1-y undoes the multiplication by 1-y.

$$k=\frac{x+y-7}{1-y}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{7-y-x}{1-y}\text{, }&y\neq 1\\k\in \mathrm{R}\text{, }&y=1\text{ and }x=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ky from both sides.

$$k-y+4-ky=x-3$$

Add y to both sides.

$$k+4-ky=x-3+y$$

Subtract 4 from both sides.

$$k-ky=x-3+y-4$$

Subtract 4 from -3 to get -7.

$$k-ky=x-7+y$$

Combine all terms containing k.

$$\left(1-y\right)k=x-7+y$$

The equation is in standard form.

$$\left(1-y\right)k=x+y-7$$

Divide both sides by 1-y.

$$\frac{\left(1-y\right)k}{1-y}=\frac{x+y-7}{1-y}$$

Dividing by 1-y undoes the multiplication by 1-y.

$$k=\frac{x+y-7}{1-y}$$

Solve for x

$$x=7+k-y-ky$$

Solution Steps

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

$$x+ky-3=k-y+4$$

Subtract ky from both sides.

$$x-3=k-y+4-ky$$

Add 3 to both sides.

$$x=k-y+4-ky+3$$

Add 4 and 3 to get 7.

$$x=k-y+7-ky$$