Solve y^4/3/x=2frac{p_{x}}{p_{y}}

$$\frac { y ^ { 4 / 3 } } { x } = 2 \frac { p _ { x } } { p _ { y } }$$

Solve for p_y (complex solution)

$$\left\{\begin{matrix}p_{y}=2y^{-\frac{4}{3}}p_{x}x\text{, }&p_{x}\neq 0\text{ and }x\neq 0\text{ and }y\neq 0\\p_{y}\neq 0\text{, }&y=0\text{ and }p_{x}=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable p_{y} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by p_{y}x, the least common multiple of x,p_{y}.

$$p_{y}y^{\frac{4}{3}}=2xp_{x}$$

The equation is in standard form.

$$y^{\frac{4}{3}}p_{y}=2p_{x}x$$

Divide both sides by y^{\frac{4}{3}}.

$$\frac{y^{\frac{4}{3}}p_{y}}{y^{\frac{4}{3}}}=\frac{2p_{x}x}{y^{\frac{4}{3}}}$$

Dividing by y^{\frac{4}{3}} undoes the multiplication by y^{\frac{4}{3}}.

$$p_{y}=\frac{2p_{x}x}{y^{\frac{4}{3}}}$$

Divide 2xp_{x} by y^{\frac{4}{3}}.

$$p_{y}=2y^{-\frac{4}{3}}p_{x}x$$

Variable p_{y} cannot be equal to 0.

$$p_{y}=2y^{-\frac{4}{3}}p_{x}x\text{, }p_{y}\neq 0$$

Solve for p_x

$$p_{x}=\frac{p_{y}y^{\frac{4}{3}}}{2x}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by p_{y}x, the least common multiple of x,p_{y}.

$$p_{y}y^{\frac{4}{3}}=2xp_{x}$$

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

$$2xp_{x}=p_{y}y^{\frac{4}{3}}$$

Divide both sides by 2x.

$$\frac{2xp_{x}}{2x}=\frac{p_{y}y^{\frac{4}{3}}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$p_{x}=\frac{p_{y}y^{\frac{4}{3}}}{2x}$$

Solve for p_y

$$\left\{\begin{matrix}p_{y}=\frac{2p_{x}x}{y^{\frac{4}{3}}}\text{, }&p_{x}\neq 0\text{ and }x\neq 0\text{ and }y\neq 0\\p_{y}\neq 0\text{, }&y=0\text{ and }p_{x}=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable p_{y} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by p_{y}x, the least common multiple of x,p_{y}.

$$p_{y}y^{\frac{4}{3}}=2xp_{x}$$

The equation is in standard form.

$$y^{\frac{4}{3}}p_{y}=2p_{x}x$$

Divide both sides by y^{\frac{4}{3}}.

$$\frac{y^{\frac{4}{3}}p_{y}}{y^{\frac{4}{3}}}=\frac{2p_{x}x}{y^{\frac{4}{3}}}$$

Dividing by y^{\frac{4}{3}} undoes the multiplication by y^{\frac{4}{3}}.

$$p_{y}=\frac{2p_{x}x}{y^{\frac{4}{3}}}$$

Variable p_{y} cannot be equal to 0.

$$p_{y}=\frac{2p_{x}x}{y^{\frac{4}{3}}}\text{, }p_{y}\neq 0$$