Solve y=(3a-1)x+1

$$y = ( 3 a - 1 ) x + 1$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{1-y-x}{3x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=3ax-x+1$$

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

$$3ax-x+1=y$$

Add x to both sides.

$$3ax+1=y+x$$

Subtract 1 from both sides.

$$3ax=y+x-1$$

The equation is in standard form.

$$3xa=x+y-1$$

Divide both sides by 3x.

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

Dividing by 3x undoes the multiplication by 3x.

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$y=3ax-x+1$$

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

$$3ax-x+1=y$$

Subtract 1 from both sides.

$$3ax-x=y-1$$

Combine all terms containing x.

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

Divide both sides by 3a-1.

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

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

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{1-y-x}{3x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=3ax-x+1$$

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

$$3ax-x+1=y$$

Add x to both sides.

$$3ax+1=y+x$$

Subtract 1 from both sides.

$$3ax=y+x-1$$

The equation is in standard form.

$$3xa=x+y-1$$

Divide both sides by 3x.

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

Dividing by 3x undoes the multiplication by 3x.

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

Solve for x

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

Steps for Solving Linear Equation

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

$$y=3ax-x+1$$

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

$$3ax-x+1=y$$

Subtract 1 from both sides.

$$3ax-x=y-1$$

Combine all terms containing x.

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

Divide both sides by 3a-1.

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

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

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