Solve 12x^2y-16xy=1

$$12 x ^ { 2 } y - 16 x y = 1$$

Solve for y

$$y=\frac{1}{4x\left(3x-4\right)}$$

$$x\neq \frac{4}{3}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Combine all terms containing y.

$$\left(12x^{2}-16x\right)y=1$$

Divide both sides by 12x^{2}-16x.

$$\frac{\left(12x^{2}-16x\right)y}{12x^{2}-16x}=\frac{1}{12x^{2}-16x}$$

Dividing by 12x^{2}-16x undoes the multiplication by 12x^{2}-16x.

$$y=\frac{1}{12x^{2}-16x}$$

Divide 1 by 12x^{2}-16x.

$$y=\frac{1}{4x\left(3x-4\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{16y^{2}+3y}}{6y}+\frac{2}{3}$$

$$x=-\frac{\sqrt{16y^{2}+3y}}{6y}+\frac{2}{3}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{16y^{2}+3y}}{6y}+\frac{2}{3}$$

$$x=-\frac{\sqrt{16y^{2}+3y}}{6y}+\frac{2}{3}\text{, }y>0\text{ or }y\leq -\frac{3}{16}$$