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

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

Solve for x

$$x=-6y$$

Steps for Solving Linear Equation

Subtract \frac{2}{3}x from both sides.

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

Combine \frac{1}{2}x and -\frac{2}{3}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x=y$$

Multiply both sides by -6.

$$\frac{-\frac{1}{6}x}{-\frac{1}{6}}=\frac{y}{-\frac{1}{6}}$$

Dividing by -\frac{1}{6} undoes the multiplication by -\frac{1}{6}.

$$x=\frac{y}{-\frac{1}{6}}$$

Divide y by -\frac{1}{6} by multiplying y by the reciprocal of -\frac{1}{6}.

$$x=-6y$$

Solve for y

$$y=-\frac{x}{6}$$

Solution Steps

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

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

Subtract \frac{2}{3}x from both sides.

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

Combine \frac{1}{2}x and -\frac{2}{3}x to get -\frac{1}{6}x.

$$y=-\frac{1}{6}x$$