Solve 2xy^2+4xy^2=24x+37y

$$2 x y ^ { 2 } + 4 x y ^ { 2 } = 24 x + 37 y$$

Solve for x (complex solution)

$$x=\frac{37y}{6\left(y^{2}-4\right)}$$

$$y\neq -2\text{ and }y\neq 2$$

Steps for Solving Linear Equation

Combine 2xy^{2} and 4xy^{2} to get 6xy^{2}.

$$6xy^{2}=24x+37y$$

Subtract 24x from both sides.

$$6xy^{2}-24x=37y$$

Combine all terms containing x.

$$\left(6y^{2}-24\right)x=37y$$

Divide both sides by 6y^{2}-24.

$$\frac{\left(6y^{2}-24\right)x}{6y^{2}-24}=\frac{37y}{6y^{2}-24}$$

Dividing by 6y^{2}-24 undoes the multiplication by 6y^{2}-24.

$$x=\frac{37y}{6y^{2}-24}$$

Divide 37y by 6y^{2}-24.

$$x=\frac{37y}{6\left(y^{2}-4\right)}$$

Solve for x

$$x=\frac{37y}{6\left(y^{2}-4\right)}$$

$$|y|\neq 2$$

Steps for Solving Linear Equation

Combine 2xy^{2} and 4xy^{2} to get 6xy^{2}.

$$6xy^{2}=24x+37y$$

Subtract 24x from both sides.

$$6xy^{2}-24x=37y$$

Combine all terms containing x.

$$\left(6y^{2}-24\right)x=37y$$

Divide both sides by 6y^{2}-24.

$$\frac{\left(6y^{2}-24\right)x}{6y^{2}-24}=\frac{37y}{6y^{2}-24}$$

Dividing by 6y^{2}-24 undoes the multiplication by 6y^{2}-24.

$$x=\frac{37y}{6y^{2}-24}$$

Divide 37y by 6y^{2}-24.

$$x=\frac{37y}{6\left(y^{2}-4\right)}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{\sqrt{576x^{2}+1369}+37}{12x}\text{; }y=\frac{-\sqrt{576x^{2}+1369}+37}{12x}\text{, }&x\neq 0\\y=0\text{, }&x=0\end{matrix}\right.$$