Solve e/x-pi/y=A

$$\frac { e } { x } - \frac { \pi } { y } = A$$

Solve for A

$$A=\frac{ey-\pi x}{xy}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by xy, the least common multiple of x,y.

$$ye-x\pi =Axy$$

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

$$Axy=ye-x\pi$$

Reorder the terms.

$$Axy=-\pi x+ey$$

The equation is in standard form.

$$xyA=ey-\pi x$$

Divide both sides by xy.

$$\frac{xyA}{xy}=\frac{ey-\pi x}{xy}$$

Dividing by xy undoes the multiplication by xy.

$$A=\frac{ey-\pi x}{xy}$$

Divide ey-\pi x by xy.

$$A=\frac{e}{x}-\frac{\pi }{y}$$

Solve for x

$$x=\frac{ey}{Ay+\pi }$$

$$y\neq 0\text{ and }\left(A=0\text{ or }y\neq -\frac{\pi }{A}\right)$$

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 xy, the least common multiple of x,y.

$$ye-x\pi =Axy$$

Subtract Axy from both sides.

$$ye-x\pi -Axy=0$$

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

$$-x\pi -Axy=-ye$$

Combine all terms containing x.

$$\left(-\pi -Ay\right)x=-ye$$

The equation is in standard form.

$$\left(-Ay-\pi \right)x=-ey$$

Divide both sides by -\pi -yA.

$$\frac{\left(-Ay-\pi \right)x}{-Ay-\pi }=-\frac{ey}{-Ay-\pi }$$

Dividing by -\pi -yA undoes the multiplication by -\pi -yA.

$$x=-\frac{ey}{-Ay-\pi }$$

Divide -ye by -\pi -yA.

$$x=\frac{ey}{Ay+\pi }$$

Variable x cannot be equal to 0.

$$x=\frac{ey}{Ay+\pi }\text{, }x\neq 0$$