Solve (k-1)x+(2k+1)y-2-k=0

$$( k - 1 ) x + ( 2 k + 1 ) y - 2 - k = 0$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{-x+y-2}{x+2y-1}\text{, }&x\neq 1-2y\\k\in \mathrm{C}\text{, }&x=-1\text{ and }y=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-1 by x.

$$kx-x+\left(2k+1\right)y-2-k=0$$

Use the distributive property to multiply 2k+1 by y.

$$kx-x+2ky+y-2-k=0$$

Add x to both sides. Anything plus zero gives itself.

$$kx+2ky+y-2-k=x$$

Subtract y from both sides.

$$kx+2ky-2-k=x-y$$

Add 2 to both sides.

$$kx+2ky-k=x-y+2$$

Combine all terms containing k.

$$\left(x+2y-1\right)k=x-y+2$$

Divide both sides by x+2y-1.

$$\frac{\left(x+2y-1\right)k}{x+2y-1}=\frac{x-y+2}{x+2y-1}$$

Dividing by x+2y-1 undoes the multiplication by x+2y-1.

$$k=\frac{x-y+2}{x+2y-1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{2ky+y-k-2}{k-1}\text{, }&k\neq 1\\x\in \mathrm{C}\text{, }&y=1\text{ and }k=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-1 by x.

$$kx-x+\left(2k+1\right)y-2-k=0$$

Use the distributive property to multiply 2k+1 by y.

$$kx-x+2ky+y-2-k=0$$

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

$$kx-x+y-2-k=-2ky$$

Subtract y from both sides.

$$kx-x-2-k=-2ky-y$$

Add 2 to both sides.

$$kx-x-k=-2ky-y+2$$

Add k to both sides.

$$kx-x=-2ky-y+2+k$$

Combine all terms containing x.

$$\left(k-1\right)x=-2ky-y+2+k$$

The equation is in standard form.

$$\left(k-1\right)x=2+k-y-2ky$$

Divide both sides by k-1.

$$\frac{\left(k-1\right)x}{k-1}=\frac{2+k-y-2ky}{k-1}$$

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

$$x=\frac{2+k-y-2ky}{k-1}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{-x+y-2}{x+2y-1}\text{, }&x\neq 1-2y\\k\in \mathrm{R}\text{, }&x=-1\text{ and }y=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-1 by x.

$$kx-x+\left(2k+1\right)y-2-k=0$$

Use the distributive property to multiply 2k+1 by y.

$$kx-x+2ky+y-2-k=0$$

Add x to both sides. Anything plus zero gives itself.

$$kx+2ky+y-2-k=x$$

Subtract y from both sides.

$$kx+2ky-2-k=x-y$$

Add 2 to both sides.

$$kx+2ky-k=x-y+2$$

Combine all terms containing k.

$$\left(x+2y-1\right)k=x-y+2$$

Divide both sides by x+2y-1.

$$\frac{\left(x+2y-1\right)k}{x+2y-1}=\frac{x-y+2}{x+2y-1}$$

Dividing by x+2y-1 undoes the multiplication by x+2y-1.

$$k=\frac{x-y+2}{x+2y-1}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2ky+y-k-2}{k-1}\text{, }&k\neq 1\\x\in \mathrm{R}\text{, }&y=1\text{ and }k=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-1 by x.

$$kx-x+\left(2k+1\right)y-2-k=0$$

Use the distributive property to multiply 2k+1 by y.

$$kx-x+2ky+y-2-k=0$$

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

$$kx-x+y-2-k=-2ky$$

Subtract y from both sides.

$$kx-x-2-k=-2ky-y$$

Add 2 to both sides.

$$kx-x-k=-2ky-y+2$$

Add k to both sides.

$$kx-x=-2ky-y+2+k$$

Combine all terms containing x.

$$\left(k-1\right)x=-2ky-y+2+k$$

The equation is in standard form.

$$\left(k-1\right)x=2+k-y-2ky$$

Divide both sides by k-1.

$$\frac{\left(k-1\right)x}{k-1}=\frac{2+k-y-2ky}{k-1}$$

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

$$x=\frac{2+k-y-2ky}{k-1}$$