Solve (2k-6)x-(4-8k)y+k-3=0

$$( 2 k - 6 ) x - ( 4 - 8 k ) y + k - 3 = 0$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{6x+4y+3}{2x+8y+1}\text{, }&x\neq -4y-\frac{1}{2}\\k\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2k-6 by x.

$$2kx-6x-\left(4-8k\right)y+k-3=0$$

Use the distributive property to multiply 4-8k by y.

$$2kx-6x-\left(4y-8ky\right)+k-3=0$$

To find the opposite of 4y-8ky, find the opposite of each term.

$$2kx-6x-4y+8ky+k-3=0$$

Add 6x to both sides. Anything plus zero gives itself.

$$2kx-4y+8ky+k-3=6x$$

Add 4y to both sides.

$$2kx+8ky+k-3=6x+4y$$

Add 3 to both sides.

$$2kx+8ky+k=6x+4y+3$$

Combine all terms containing k.

$$\left(2x+8y+1\right)k=6x+4y+3$$

Divide both sides by 2x+8y+1.

$$\frac{\left(2x+8y+1\right)k}{2x+8y+1}=\frac{6x+4y+3}{2x+8y+1}$$

Dividing by 2x+8y+1 undoes the multiplication by 2x+8y+1.

$$k=\frac{6x+4y+3}{2x+8y+1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{8ky-4y+k-3}{2\left(k-3\right)}\text{, }&k\neq 3\\x\in \mathrm{C}\text{, }&y=0\text{ and }k=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2k-6 by x.

$$2kx-6x-\left(4-8k\right)y+k-3=0$$

Use the distributive property to multiply 4-8k by y.

$$2kx-6x-\left(4y-8ky\right)+k-3=0$$

To find the opposite of 4y-8ky, find the opposite of each term.

$$2kx-6x-4y+8ky+k-3=0$$

Add 4y to both sides. Anything plus zero gives itself.

$$2kx-6x+8ky+k-3=4y$$

Subtract 8ky from both sides.

$$2kx-6x+k-3=4y-8ky$$

Subtract k from both sides.

$$2kx-6x-3=4y-8ky-k$$

Add 3 to both sides.

$$2kx-6x=4y-8ky-k+3$$

Combine all terms containing x.

$$\left(2k-6\right)x=4y-8ky-k+3$$

The equation is in standard form.

$$\left(2k-6\right)x=3-k+4y-8ky$$

Divide both sides by 2k-6.

$$\frac{\left(2k-6\right)x}{2k-6}=\frac{3-k+4y-8ky}{2k-6}$$

Dividing by 2k-6 undoes the multiplication by 2k-6.

$$x=\frac{3-k+4y-8ky}{2k-6}$$

Divide 4y-8ky-k+3 by 2k-6.

$$x=\frac{3-k+4y-8ky}{2\left(k-3\right)}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{6x+4y+3}{2x+8y+1}\text{, }&x\neq -4y-\frac{1}{2}\\k\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2k-6 by x.

$$2kx-6x-\left(4-8k\right)y+k-3=0$$

Use the distributive property to multiply 4-8k by y.

$$2kx-6x-\left(4y-8ky\right)+k-3=0$$

To find the opposite of 4y-8ky, find the opposite of each term.

$$2kx-6x-4y+8ky+k-3=0$$

Add 6x to both sides. Anything plus zero gives itself.

$$2kx-4y+8ky+k-3=6x$$

Add 4y to both sides.

$$2kx+8ky+k-3=6x+4y$$

Add 3 to both sides.

$$2kx+8ky+k=6x+4y+3$$

Combine all terms containing k.

$$\left(2x+8y+1\right)k=6x+4y+3$$

Divide both sides by 2x+8y+1.

$$\frac{\left(2x+8y+1\right)k}{2x+8y+1}=\frac{6x+4y+3}{2x+8y+1}$$

Dividing by 2x+8y+1 undoes the multiplication by 2x+8y+1.

$$k=\frac{6x+4y+3}{2x+8y+1}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{8ky-4y+k-3}{2\left(k-3\right)}\text{, }&k\neq 3\\x\in \mathrm{R}\text{, }&y=0\text{ and }k=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2k-6 by x.

$$2kx-6x-\left(4-8k\right)y+k-3=0$$

Use the distributive property to multiply 4-8k by y.

$$2kx-6x-\left(4y-8ky\right)+k-3=0$$

To find the opposite of 4y-8ky, find the opposite of each term.

$$2kx-6x-4y+8ky+k-3=0$$

Add 4y to both sides. Anything plus zero gives itself.

$$2kx-6x+8ky+k-3=4y$$

Subtract 8ky from both sides.

$$2kx-6x+k-3=4y-8ky$$

Subtract k from both sides.

$$2kx-6x-3=4y-8ky-k$$

Add 3 to both sides.

$$2kx-6x=4y-8ky-k+3$$

Combine all terms containing x.

$$\left(2k-6\right)x=4y-8ky-k+3$$

The equation is in standard form.

$$\left(2k-6\right)x=3-k+4y-8ky$$

Divide both sides by 2k-6.

$$\frac{\left(2k-6\right)x}{2k-6}=\frac{3-k+4y-8ky}{2k-6}$$

Dividing by 2k-6 undoes the multiplication by 2k-6.

$$x=\frac{3-k+4y-8ky}{2k-6}$$

Divide 4y-8ky-k+3 by 2k-6.

$$x=\frac{3-k+4y-8ky}{2\left(k-3\right)}$$