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

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

Solve for I

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 3P_{x}P_{y}, the least common multiple of P_{y},3P_{x}.

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

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

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

Multiply 3 and 2 to get 6.

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

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

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

Cancel out 3 in both numerator and denominator.

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

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

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

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

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

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

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

The equation is in standard form.

$$2P_{x}I=3P_{x}P_{y}y$$

Divide both sides by 2P_{x}.

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

Dividing by 2P_{x} undoes the multiplication by 2P_{x}.

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

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

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

Solve for P_x

$$P_{x}\neq 0$$

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