Solve ay+x/x=4-y

$$\frac { a y + x } { x } = 4 - y$$

Solve for a

$$a=-\frac{x\left(y-3\right)}{y}$$

$$y\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$ay+x=x\times 4-yx$$

Subtract x from both sides.

$$ay=x\times 4-yx-x$$

Combine x\times 4 and -x to get 3x.

$$ay=3x-yx$$

The equation is in standard form.

$$ya=3x-xy$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{x\left(3-y\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{x\left(3-y\right)}{y}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{ay}{y-3}\text{, }&y\neq 0\text{ and }a\neq 0\text{ and }y\neq 3\\x\neq 0\text{, }&a=0\text{ and }y=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$ay+x=x\times 4-yx$$

Subtract x\times 4 from both sides.

$$ay+x-x\times 4=-yx$$

Combine x and -x\times 4 to get -3x.

$$ay-3x=-yx$$

Add yx to both sides.

$$ay-3x+yx=0$$

Subtract ay from both sides. Anything subtracted from zero gives its negation.

$$-3x+yx=-ay$$

Reorder the terms.

$$xy-3x=-ay$$

Combine all terms containing x.

$$\left(y-3\right)x=-ay$$

Divide both sides by -3+y.

$$\frac{\left(y-3\right)x}{y-3}=-\frac{ay}{y-3}$$

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

$$x=-\frac{ay}{y-3}$$

Variable x cannot be equal to 0.

$$x=-\frac{ay}{y-3}\text{, }x\neq 0$$