Solve y=x+72-93xdiv24y+4z

$$y=x+72-93x \div 24y+4z$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{8\left(72+4z-y\right)}{8-31y}\text{, }&y\neq \frac{8}{31}\\x\in \mathrm{C}\text{, }&y=\frac{8}{31}\text{ and }z=-\frac{556}{31}\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide 93x by 24 to get \frac{31}{8}x.

$$y=x+72-\frac{31}{8}xy+4z$$

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

$$x+72-\frac{31}{8}xy+4z=y$$

Subtract 72 from both sides.

$$x-\frac{31}{8}xy+4z=y-72$$

Subtract 4z from both sides.

$$x-\frac{31}{8}xy=y-72-4z$$

Combine all terms containing x.

$$\left(1-\frac{31}{8}y\right)x=y-72-4z$$

The equation is in standard form.

$$\left(-\frac{31y}{8}+1\right)x=y-4z-72$$

Divide both sides by 1-\frac{31}{8}y.

$$\frac{\left(-\frac{31y}{8}+1\right)x}{-\frac{31y}{8}+1}=\frac{y-4z-72}{-\frac{31y}{8}+1}$$

Dividing by 1-\frac{31}{8}y undoes the multiplication by 1-\frac{31}{8}y.

$$x=\frac{y-4z-72}{-\frac{31y}{8}+1}$$

Divide y-72-4z by 1-\frac{31}{8}y.

$$x=\frac{8\left(y-4z-72\right)}{8-31y}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{8\left(x+4z+72\right)}{31x+8}\text{, }&x\neq -\frac{8}{31}\\y\in \mathrm{C}\text{, }&x=-\frac{8}{31}\text{ and }z=-\frac{556}{31}\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide 93x by 24 to get \frac{31}{8}x.

$$y=x+72-\frac{31}{8}xy+4z$$

Add \frac{31}{8}xy to both sides.

$$y+\frac{31}{8}xy=x+72+4z$$

Combine all terms containing y.

$$\left(1+\frac{31}{8}x\right)y=x+72+4z$$

The equation is in standard form.

$$\left(\frac{31x}{8}+1\right)y=x+4z+72$$

Divide both sides by 1+\frac{31}{8}x.

$$\frac{\left(\frac{31x}{8}+1\right)y}{\frac{31x}{8}+1}=\frac{x+4z+72}{\frac{31x}{8}+1}$$

Dividing by 1+\frac{31}{8}x undoes the multiplication by 1+\frac{31}{8}x.

$$y=\frac{x+4z+72}{\frac{31x}{8}+1}$$

Divide x+72+4z by 1+\frac{31}{8}x.

$$y=\frac{8\left(x+4z+72\right)}{31x+8}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{8\left(72+4z-y\right)}{8-31y}\text{, }&y\neq \frac{8}{31}\\x\in \mathrm{R}\text{, }&y=\frac{8}{31}\text{ and }z=-\frac{556}{31}\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide 93x by 24 to get \frac{31}{8}x.

$$y=x+72-\frac{31}{8}xy+4z$$

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

$$x+72-\frac{31}{8}xy+4z=y$$

Subtract 72 from both sides.

$$x-\frac{31}{8}xy+4z=y-72$$

Subtract 4z from both sides.

$$x-\frac{31}{8}xy=y-72-4z$$

Combine all terms containing x.

$$\left(1-\frac{31}{8}y\right)x=y-72-4z$$

The equation is in standard form.

$$\left(-\frac{31y}{8}+1\right)x=y-4z-72$$

Divide both sides by 1-\frac{31}{8}y.

$$\frac{\left(-\frac{31y}{8}+1\right)x}{-\frac{31y}{8}+1}=\frac{y-4z-72}{-\frac{31y}{8}+1}$$

Dividing by 1-\frac{31}{8}y undoes the multiplication by 1-\frac{31}{8}y.

$$x=\frac{y-4z-72}{-\frac{31y}{8}+1}$$

Divide y-72-4z by 1-\frac{31}{8}y.

$$x=\frac{8\left(y-4z-72\right)}{8-31y}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{8\left(x+4z+72\right)}{31x+8}\text{, }&x\neq -\frac{8}{31}\\y\in \mathrm{R}\text{, }&x=-\frac{8}{31}\text{ and }z=-\frac{556}{31}\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide 93x by 24 to get \frac{31}{8}x.

$$y=x+72-\frac{31}{8}xy+4z$$

Add \frac{31}{8}xy to both sides.

$$y+\frac{31}{8}xy=x+72+4z$$

Combine all terms containing y.

$$\left(1+\frac{31}{8}x\right)y=x+72+4z$$

The equation is in standard form.

$$\left(\frac{31x}{8}+1\right)y=x+4z+72$$

Divide both sides by 1+\frac{31}{8}x.

$$\frac{\left(\frac{31x}{8}+1\right)y}{\frac{31x}{8}+1}=\frac{x+4z+72}{\frac{31x}{8}+1}$$

Dividing by 1+\frac{31}{8}x undoes the multiplication by 1+\frac{31}{8}x.

$$y=\frac{x+4z+72}{\frac{31x}{8}+1}$$

Divide x+72+4z by 1+\frac{31}{8}x.

$$y=\frac{8\left(x+4z+72\right)}{31x+8}$$