Solve y=-2x+1/3

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

Solve for x

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

Steps for Solving Linear Equation

Divide each term of 2x+1 by 3 to get \frac{2}{3}x+\frac{1}{3}.

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

To find the opposite of \frac{2}{3}x+\frac{1}{3}, find the opposite of each term.

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

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

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

Add \frac{1}{3} to both sides.

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

Divide both sides of the equation by -\frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

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

Dividing by -\frac{2}{3} undoes the multiplication by -\frac{2}{3}.

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

Divide y+\frac{1}{3} by -\frac{2}{3} by multiplying y+\frac{1}{3} by the reciprocal of -\frac{2}{3}.

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

Solve for y

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

Solution Steps

Divide each term of 2x+1 by 3 to get \frac{2}{3}x+\frac{1}{3}.

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

To find the opposite of \frac{2}{3}x+\frac{1}{3}, find the opposite of each term.

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