Solve y=frac{2P_{x}}{P_{y}}*T/3P_{x}

$$y = \frac { 2 P _ { x } } { P _ { y } } \cdot \frac { T } { 3 P _ { x } }$$

Solve for P_y

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

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 3P_{x}P_{y}, the least common multiple of P_{y},3P_{x}.

$$y\times 3P_{x}P_{y}=3P_{x}\times 2P_{x}\times \frac{T}{3P_{x}}$$

Multiply P_{x} and P_{x} to get P_{x}^{2}.

$$y\times 3P_{x}P_{y}=3P_{x}^{2}\times 2\times \frac{T}{3P_{x}}$$

Multiply 3 and 2 to get 6.

$$y\times 3P_{x}P_{y}=6P_{x}^{2}\times \frac{T}{3P_{x}}$$

Express 6\times \frac{T}{3P_{x}} as a single fraction.

$$y\times 3P_{x}P_{y}=\frac{6T}{3P_{x}}P_{x}^{2}$$

Cancel out 3 in both numerator and denominator.

$$y\times 3P_{x}P_{y}=\frac{2T}{P_{x}}P_{x}^{2}$$

Express \frac{2T}{P_{x}}P_{x}^{2} as a single fraction.

$$y\times 3P_{x}P_{y}=\frac{2TP_{x}^{2}}{P_{x}}$$

Cancel out P_{x} in both numerator and denominator.

$$y\times 3P_{x}P_{y}=2P_{x}T$$

The equation is in standard form.

$$3P_{x}yP_{y}=2P_{x}T$$

Divide both sides by 3yP_{x}.

$$\frac{3P_{x}yP_{y}}{3P_{x}y}=\frac{2P_{x}T}{3P_{x}y}$$

Dividing by 3yP_{x} undoes the multiplication by 3yP_{x}.

$$P_{y}=\frac{2P_{x}T}{3P_{x}y}$$

Divide 2P_{x}T by 3yP_{x}.

$$P_{y}=\frac{2T}{3y}$$

Variable P_{y} cannot be equal to 0.

$$P_{y}=\frac{2T}{3y}\text{, }P_{y}\neq 0$$

Solve for P_x

$$P_{x}\neq 0$$

$$\left(y=0\text{ and }T=0\text{ and }P_{y}\neq 0\right)\text{ or }\left(P_{y}=\frac{2T}{3y}\text{ and }y\neq 0\text{ and }T\neq 0\right)$$