Solve 2xy1y^2=6

$$2 x y 1 y ^ { 2 } = 6$$

Solve for x

$$x=\frac{3}{y_{1}y^{2}}$$

$$y\neq 0\text{ and }y_{1}\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$2y_{1}y^{2}x=6$$

Divide both sides by 2y_{1}y^{2}.

$$\frac{2y_{1}y^{2}x}{2y_{1}y^{2}}=\frac{6}{2y_{1}y^{2}}$$

Dividing by 2y_{1}y^{2} undoes the multiplication by 2y_{1}y^{2}.

$$x=\frac{6}{2y_{1}y^{2}}$$

Divide 6 by 2y_{1}y^{2}.

$$x=\frac{3}{y_{1}y^{2}}$$

Solve for y (complex solution)

$$y=-\sqrt{3}x^{-\frac{1}{2}}y_{1}^{-\frac{1}{2}}$$

$$y=\sqrt{3}x^{-\frac{1}{2}}y_{1}^{-\frac{1}{2}}\text{, }y_{1}\neq 0\text{ and }x\neq 0$$

Solve for y

$$y=\sqrt{\frac{3}{xy_{1}}}$$

$$y=-\sqrt{\frac{3}{xy_{1}}}\text{, }\left(y_{1}>0\text{ and }x>0\right)\text{ or }\left(x<0\text{ and }y_{1}<0\right)$$