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

$$2 x - 2 + 3 y = 2 y + 1 + 3 x$$

Solve for x

$$x=y-3$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

$$2x-2+3y-3x=2y+1$$

Combine 2x and -3x to get -x.

$$-x-2+3y=2y+1$$

Add 2 to both sides.

$$-x+3y=2y+1+2$$

Add 1 and 2 to get 3.

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

Subtract 3y from both sides.

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

Combine 2y and -3y to get -y.

$$-x=-y+3$$

The equation is in standard form.

$$-x=3-y$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -y+3 by -1.

$$x=y-3$$

Solve for y

$$y=x+3$$

Solution Steps

Subtract 2y from both sides.

$$2x-2+3y-2y=1+3x$$

Combine 3y and -2y to get y.

$$2x-2+y=1+3x$$

Subtract 2x from both sides.

$$-2+y=1+3x-2x$$

Combine 3x and -2x to get x.

$$-2+y=1+x$$

Add 2 to both sides.

$$y=1+x+2$$

Add 1 and 2 to get 3.

$$y=3+x$$