Solve 2x+3y-4z=145-xy

$$2x+3y-4z = 145-xy$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{3y-4z-145}{y+2}\text{, }&y\neq -2\\x\in \mathrm{R}\text{, }&y=-2\text{ and }z=-\frac{151}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Add xy to both sides.

$$2x+3y-4z+xy=145$$

Subtract 3y from both sides.

$$2x-4z+xy=145-3y$$

Add 4z to both sides.

$$2x+xy=145-3y+4z$$

Combine all terms containing x.

$$\left(2+y\right)x=145-3y+4z$$

The equation is in standard form.

$$\left(y+2\right)x=145+4z-3y$$

Divide both sides by y+2.

$$\frac{\left(y+2\right)x}{y+2}=\frac{145+4z-3y}{y+2}$$

Dividing by y+2 undoes the multiplication by y+2.

$$x=\frac{145+4z-3y}{y+2}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{2x-4z-145}{x+3}\text{, }&x\neq -3\\y\in \mathrm{R}\text{, }&x=-3\text{ and }z=-\frac{151}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Add xy to both sides.

$$2x+3y-4z+xy=145$$

Subtract 2x from both sides.

$$3y-4z+xy=145-2x$$

Add 4z to both sides.

$$3y+xy=145-2x+4z$$

Combine all terms containing y.

$$\left(3+x\right)y=145-2x+4z$$

The equation is in standard form.

$$\left(x+3\right)y=145+4z-2x$$

Divide both sides by 3+x.

$$\frac{\left(x+3\right)y}{x+3}=\frac{145+4z-2x}{x+3}$$

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

$$y=\frac{145+4z-2x}{x+3}$$