Solve r_{1}*x^2*y^2=4

$$r _ { 1 } \cdot x ^ { 2 } \cdot y ^ { 2 } = 4$$

Solve for r_1

$$r_{1}=\frac{4}{\left(xy\right)^{2}}$$

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

Steps for Solving Linear Equation

The equation is in standard form.

$$x^{2}y^{2}r_{1}=4$$

Divide both sides by x^{2}y^{2}.

$$\frac{x^{2}y^{2}r_{1}}{x^{2}y^{2}}=\frac{4}{x^{2}y^{2}}$$

Dividing by x^{2}y^{2} undoes the multiplication by x^{2}y^{2}.

$$r_{1}=\frac{4}{x^{2}y^{2}}$$

Divide 4 by x^{2}y^{2}.

$$r_{1}=\frac{4}{\left(xy\right)^{2}}$$

Solve for x (complex solution)

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

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

Solve for x

$$x=\frac{2}{\sqrt{r_{1}}y}$$

$$x=-\frac{2}{\sqrt{r_{1}}y}\text{, }y\neq 0\text{ and }r_{1}>0$$