Solve 4x+3y=5yP(22)

$$4x+3y = 5yP(22)$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=\frac{2x}{55y}+\frac{3}{110}\text{, }&y\neq 0\\P\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 5 and 22 to get 110.

$$4x+3y=110yP$$

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

$$110yP=4x+3y$$

Divide both sides by 110y.

$$\frac{110yP}{110y}=\frac{4x+3y}{110y}$$

Dividing by 110y undoes the multiplication by 110y.

$$P=\frac{4x+3y}{110y}$$

Divide 4x+3y by 110y.

$$P=\frac{2x}{55y}+\frac{3}{110}$$

Solve for P

$$\left\{\begin{matrix}P=\frac{2x}{55y}+\frac{3}{110}\text{, }&y\neq 0\\P\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 5 and 22 to get 110.

$$4x+3y=110yP$$

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

$$110yP=4x+3y$$

Divide both sides by 110y.

$$\frac{110yP}{110y}=\frac{4x+3y}{110y}$$

Dividing by 110y undoes the multiplication by 110y.

$$P=\frac{4x+3y}{110y}$$

Divide 4x+3y by 110y.

$$P=\frac{2x}{55y}+\frac{3}{110}$$

Solve for x

$$x=\frac{y\left(110P-3\right)}{4}$$

Steps for Solving Linear Equation

Multiply 5 and 22 to get 110.

$$4x+3y=110yP$$

Subtract 3y from both sides.

$$4x=110yP-3y$$

The equation is in standard form.

$$4x=110Py-3y$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{y\left(110P-3\right)}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{y\left(110P-3\right)}{4}$$

Divide y\left(-3+110P\right) by 4.

$$x=\frac{55Py}{2}-\frac{3y}{4}$$