Solve 2x-y+1/x-y+3=k

$$\frac { 2 x - y + 1 } { x - y + 3 } = k$$

Solve for k

$$k=-\frac{2x-y+1}{-x+y-3}$$

$$x\neq y-3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-y+3.

$$2x-y+1=k\left(x-y+3\right)$$

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

$$2x-y+1=kx-ky+3k$$

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

$$kx-ky+3k=2x-y+1$$

Combine all terms containing k.

$$\left(x-y+3\right)k=2x-y+1$$

Divide both sides by x-y+3.

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

Dividing by x-y+3 undoes the multiplication by x-y+3.

$$k=\frac{2x-y+1}{x-y+3}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{ky-y-3k+1}{2-k}\text{, }&y\neq 5\text{ and }k\neq 2\\x\neq 2\text{, }&k=2\text{ and }y=5\end{matrix}\right.$$