Solve 7xz+9=yz+3xy

$$7xz+9=yz+3xy$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{9-yz}{7z-3y}\text{, }&z\neq \frac{3y}{7}\\x\in \mathrm{C}\text{, }&\left(y=\sqrt{21}\text{ and }z=\frac{3\sqrt{21}}{7}\right)\text{ or }\left(y=-\sqrt{21}\text{ and }z=-\frac{3\sqrt{21}}{7}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3xy from both sides.

$$7xz+9-3xy=yz$$

Subtract 9 from both sides.

$$7xz-3xy=yz-9$$

Combine all terms containing x.

$$\left(7z-3y\right)x=yz-9$$

Divide both sides by -3y+7z.

$$\frac{\left(7z-3y\right)x}{7z-3y}=\frac{yz-9}{7z-3y}$$

Dividing by -3y+7z undoes the multiplication by -3y+7z.

$$x=\frac{yz-9}{7z-3y}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{7xz+9}{3x+z}\text{, }&x\neq -\frac{z}{3}\\y\in \mathrm{C}\text{, }&\left(z=-\frac{3\sqrt{21}}{7}\text{ and }x=\frac{\sqrt{21}}{7}\right)\text{ or }\left(z=\frac{3\sqrt{21}}{7}\text{ and }x=-\frac{\sqrt{21}}{7}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$yz+3xy=7xz+9$$

Combine all terms containing y.

$$\left(z+3x\right)y=7xz+9$$

The equation is in standard form.

$$\left(3x+z\right)y=7xz+9$$

Divide both sides by z+3x.

$$\frac{\left(3x+z\right)y}{3x+z}=\frac{7xz+9}{3x+z}$$

Dividing by z+3x undoes the multiplication by z+3x.

$$y=\frac{7xz+9}{3x+z}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{9-yz}{7z-3y}\text{, }&z\neq \frac{3y}{7}\\x\in \mathrm{R}\text{, }&\left(y=-\sqrt{21}\text{ and }z=-\frac{3\sqrt{21}}{7}\right)\text{ or }\left(y=\sqrt{21}\text{ and }z=\frac{3\sqrt{21}}{7}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3xy from both sides.

$$7xz+9-3xy=yz$$

Subtract 9 from both sides.

$$7xz-3xy=yz-9$$

Combine all terms containing x.

$$\left(7z-3y\right)x=yz-9$$

Divide both sides by -3y+7z.

$$\frac{\left(7z-3y\right)x}{7z-3y}=\frac{yz-9}{7z-3y}$$

Dividing by -3y+7z undoes the multiplication by -3y+7z.

$$x=\frac{yz-9}{7z-3y}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{7xz+9}{3x+z}\text{, }&x\neq -\frac{z}{3}\\y\in \mathrm{R}\text{, }&\left(z=\frac{3\sqrt{21}}{7}\text{ and }x=-\frac{\sqrt{21}}{7}\right)\text{ or }\left(z=-\frac{3\sqrt{21}}{7}\text{ and }x=\frac{\sqrt{21}}{7}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$yz+3xy=7xz+9$$

Combine all terms containing y.

$$\left(z+3x\right)y=7xz+9$$

The equation is in standard form.

$$\left(3x+z\right)y=7xz+9$$

Divide both sides by z+3x.

$$\frac{\left(3x+z\right)y}{3x+z}=\frac{7xz+9}{3x+z}$$

Dividing by z+3x undoes the multiplication by z+3x.

$$y=\frac{7xz+9}{3x+z}$$