Solve E=(p_{2}-p_{1})y/p_{1}y

$$E = ( p _ { 2 } - p _ { 1 } ) y / p _ { 1 } y$$

Solve for p_1

$$\left\{\begin{matrix}p_{1}=\frac{p_{2}y^{2}}{y^{2}+E}\text{, }&p_{2}\neq 0\text{ and }y\neq 0\text{ and }E\neq -y^{2}\\p_{1}\neq 0\text{, }&\left(E=0\text{ and }y=0\right)\text{ or }\left(p_{2}=0\text{ and }E=-y^{2}\text{ and }y\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable p_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by p_{1}.

$$Ep_{1}=\left(p_{2}-p_{1}\right)yy$$

Multiply y and y to get y^{2}.

$$Ep_{1}=\left(p_{2}-p_{1}\right)y^{2}$$

Use the distributive property to multiply p_{2}-p_{1} by y^{2}.

$$Ep_{1}=p_{2}y^{2}-p_{1}y^{2}$$

Add p_{1}y^{2} to both sides.

$$Ep_{1}+p_{1}y^{2}=p_{2}y^{2}$$

Combine all terms containing p_{1}.

$$\left(E+y^{2}\right)p_{1}=p_{2}y^{2}$$

The equation is in standard form.

$$\left(y^{2}+E\right)p_{1}=p_{2}y^{2}$$

Divide both sides by E+y^{2}.

$$\frac{\left(y^{2}+E\right)p_{1}}{y^{2}+E}=\frac{p_{2}y^{2}}{y^{2}+E}$$

Dividing by E+y^{2} undoes the multiplication by E+y^{2}.

$$p_{1}=\frac{p_{2}y^{2}}{y^{2}+E}$$

Variable p_{1} cannot be equal to 0.

$$p_{1}=\frac{p_{2}y^{2}}{y^{2}+E}\text{, }p_{1}\neq 0$$

Solve for E

$$E=-\frac{\left(p_{1}-p_{2}\right)y^{2}}{p_{1}}$$

$$p_{1}\neq 0$$