Solve y=(3a+1)*x+2

$$y = ( 3 a + 1 ) \cdot x + 2$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x-y+2}{3x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3a+1 by x.

$$y=3ax+x+2$$

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

$$3ax+x+2=y$$

Subtract x from both sides.

$$3ax+2=y-x$$

Subtract 2 from both sides.

$$3ax=y-x-2$$

The equation is in standard form.

$$3xa=-x+y-2$$

Divide both sides by 3x.

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

Dividing by 3x undoes the multiplication by 3x.

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply 3a+1 by x.

$$y=3ax+x+2$$

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

$$3ax+x+2=y$$

Subtract 2 from both sides.

$$3ax+x=y-2$$

Combine all terms containing x.

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

Divide both sides by 3a+1.

$$\frac{\left(3a+1\right)x}{3a+1}=\frac{y-2}{3a+1}$$

Dividing by 3a+1 undoes the multiplication by 3a+1.

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{x-y+2}{3x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3a+1 by x.

$$y=3ax+x+2$$

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

$$3ax+x+2=y$$

Subtract x from both sides.

$$3ax+2=y-x$$

Subtract 2 from both sides.

$$3ax=y-x-2$$

The equation is in standard form.

$$3xa=-x+y-2$$

Divide both sides by 3x.

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

Dividing by 3x undoes the multiplication by 3x.

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply 3a+1 by x.

$$y=3ax+x+2$$

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

$$3ax+x+2=y$$

Subtract 2 from both sides.

$$3ax+x=y-2$$

Combine all terms containing x.

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

Divide both sides by 3a+1.

$$\frac{\left(3a+1\right)x}{3a+1}=\frac{y-2}{3a+1}$$

Dividing by 3a+1 undoes the multiplication by 3a+1.

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