Solve x=-3y-z/2y+1

$$x = \frac { - 3 y - z } { 2 y + 1 }$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{x+z}{2x+3}\text{, }&z\neq \frac{3}{2}\text{ and }x\neq -\frac{3}{2}\\y\neq -\frac{1}{2}\text{, }&x=-\frac{3}{2}\text{ and }z=\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable y cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2y+1.

$$x\left(2y+1\right)=-3y-z$$

Use the distributive property to multiply x by 2y+1.

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

Add 3y to both sides.

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

Subtract x from both sides.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 2x+3.

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

Dividing by 2x+3 undoes the multiplication by 2x+3.

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

Divide -z-x by 2x+3.

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

Variable y cannot be equal to -\frac{1}{2}.

$$y=-\frac{x+z}{2x+3}\text{, }y\neq -\frac{1}{2}$$

Solve for x

$$x=-\frac{3y+z}{2y+1}$$

$$y\neq -\frac{1}{2}$$