Solve 3x*sqrt{y}*7-14x+22y=16

$$3x \times \sqrt{ y } \times 7-14x+22y=16$$

Solve for x (complex solution)

$$x=-\frac{2\left(11y-8\right)}{7\left(3\sqrt{y}-2\right)}$$

$$y\neq \frac{4}{9}$$

Steps for Solving Linear Equation

Multiply 3 and 7 to get 21.

$$21x\sqrt{y}-14x+22y=16$$

Subtract 22y from both sides.

$$21x\sqrt{y}-14x=16-22y$$

Combine all terms containing x.

$$\left(21\sqrt{y}-14\right)x=16-22y$$

Divide both sides by 21\sqrt{y}-14.

$$\frac{\left(21\sqrt{y}-14\right)x}{21\sqrt{y}-14}=\frac{16-22y}{21\sqrt{y}-14}$$

Dividing by 21\sqrt{y}-14 undoes the multiplication by 21\sqrt{y}-14.

$$x=\frac{16-22y}{21\sqrt{y}-14}$$

Divide 16-22y by 21\sqrt{y}-14.

$$x=\frac{16-22y}{7\left(3\sqrt{y}-2\right)}$$

Solve for x

$$x=\frac{2\left(8-11y\right)}{7\left(3\sqrt{y}-2\right)}$$

$$y\neq \frac{4}{9}\text{ and }y\geq 0$$

Steps for Solving Linear Equation

Multiply 3 and 7 to get 21.

$$21x\sqrt{y}-14x+22y=16$$

Subtract 22y from both sides.

$$21x\sqrt{y}-14x=16-22y$$

Combine all terms containing x.

$$\left(21\sqrt{y}-14\right)x=16-22y$$

Divide both sides by 21\sqrt{y}-14.

$$\frac{\left(21\sqrt{y}-14\right)x}{21\sqrt{y}-14}=\frac{16-22y}{21\sqrt{y}-14}$$

Dividing by 21\sqrt{y}-14 undoes the multiplication by 21\sqrt{y}-14.

$$x=\frac{16-22y}{21\sqrt{y}-14}$$

Divide 16-22y by 21\sqrt{y}-14.

$$x=\frac{16-22y}{7\left(3\sqrt{y}-2\right)}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=0\text{, }&x=-\frac{8}{7}\\y=\frac{\left(\sqrt{441x^{2}+1232x+1408}+21x\right)^{2}}{1936}\text{, }&arg(\frac{\sqrt{441x^{2}+1232x+1408}+21x}{44})\geq \pi \\y=\frac{\left(-\sqrt{441x^{2}+1232x+1408}+21x\right)^{2}}{1936}\text{, }&arg(\frac{-\sqrt{441x^{2}+1232x+1408}+21x}{44})\geq \pi \end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\frac{\left(-\sqrt{441x^{2}+1232x+1408}+21x\right)^{2}}{1936}\text{, }&-\frac{-\sqrt{441x^{2}+1232x+1408}+21x}{44}\geq 0\\y=\frac{\left(\sqrt{441x^{2}+1232x+1408}+21x\right)^{2}}{1936}\text{, }&-\frac{\sqrt{441x^{2}+1232x+1408}+21x}{44}\geq 0\end{matrix}\right.$$