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

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

Solve for k

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

$$y\neq x$$

Steps for Solving Linear Equation

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

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

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

$$y+x=-xk+yk$$

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

$$-xk+yk=y+x$$

Combine all terms containing k.

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

The equation is in standard form.

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

Divide both sides by y-x.

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

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

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

Solve for x

$$\left\{\begin{matrix}x=-\frac{y\left(1-k\right)}{k+1}\text{, }&y\neq 0\text{ and }k\neq -1\\x\neq 0\text{, }&y=0\text{ and }k=-1\end{matrix}\right.$$