Solve (k-3)x+(4-k)y+1=0

$$( k - 3 ) x + ( 4 - k ) y + 1 = 0$$

Solve for k (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply k-3 by x.

$$kx-3x+\left(4-k\right)y+1=0$$

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

$$kx-3x+4y-ky+1=0$$

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

$$kx+4y-ky+1=3x$$

Subtract 4y from both sides.

$$kx-ky+1=3x-4y$$

Subtract 1 from both sides.

$$kx-ky=3x-4y-1$$

Combine all terms containing k.

$$\left(x-y\right)k=3x-4y-1$$

Divide both sides by x-y.

$$\frac{\left(x-y\right)k}{x-y}=\frac{3x-4y-1}{x-y}$$

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

$$k=\frac{3x-4y-1}{x-y}$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply k-3 by x.

$$kx-3x+\left(4-k\right)y+1=0$$

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

$$kx-3x+4y-ky+1=0$$

Subtract 4y from both sides. Anything subtracted from zero gives its negation.

$$kx-3x-ky+1=-4y$$

Add ky to both sides.

$$kx-3x+1=-4y+ky$$

Subtract 1 from both sides.

$$kx-3x=-4y+ky-1$$

Combine all terms containing x.

$$\left(k-3\right)x=-4y+ky-1$$

The equation is in standard form.

$$\left(k-3\right)x=ky-4y-1$$

Divide both sides by k-3.

$$\frac{\left(k-3\right)x}{k-3}=\frac{ky-4y-1}{k-3}$$

Dividing by k-3 undoes the multiplication by k-3.

$$x=\frac{ky-4y-1}{k-3}$$

Solve for k

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

Steps for Solving Linear Equation

Use the distributive property to multiply k-3 by x.

$$kx-3x+\left(4-k\right)y+1=0$$

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

$$kx-3x+4y-ky+1=0$$

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

$$kx+4y-ky+1=3x$$

Subtract 4y from both sides.

$$kx-ky+1=3x-4y$$

Subtract 1 from both sides.

$$kx-ky=3x-4y-1$$

Combine all terms containing k.

$$\left(x-y\right)k=3x-4y-1$$

Divide both sides by x-y.

$$\frac{\left(x-y\right)k}{x-y}=\frac{3x-4y-1}{x-y}$$

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

$$k=\frac{3x-4y-1}{x-y}$$

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply k-3 by x.

$$kx-3x+\left(4-k\right)y+1=0$$

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

$$kx-3x+4y-ky+1=0$$

Subtract 4y from both sides. Anything subtracted from zero gives its negation.

$$kx-3x-ky+1=-4y$$

Add ky to both sides.

$$kx-3x+1=-4y+ky$$

Subtract 1 from both sides.

$$kx-3x=-4y+ky-1$$

Combine all terms containing x.

$$\left(k-3\right)x=-4y+ky-1$$

The equation is in standard form.

$$\left(k-3\right)x=ky-4y-1$$

Divide both sides by k-3.

$$\frac{\left(k-3\right)x}{k-3}=\frac{ky-4y-1}{k-3}$$

Dividing by k-3 undoes the multiplication by k-3.

$$x=\frac{ky-4y-1}{k-3}$$