Solve 2/3x-1=6y+(x-y)

$$\frac{ 2 }{ 3 } x-1=6y+(x-y)$$

Solve for x

$$x=-15y-3$$

Steps for Solving Linear Equation

Combine 6y and -y to get 5y.

$$\frac{2}{3}x-1=5y+x$$

Subtract x from both sides.

$$\frac{2}{3}x-1-x=5y$$

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

$$-\frac{1}{3}x-1=5y$$

Add 1 to both sides.

$$-\frac{1}{3}x=5y+1$$

Multiply both sides by -3.

$$\frac{-\frac{1}{3}x}{-\frac{1}{3}}=\frac{5y+1}{-\frac{1}{3}}$$

Dividing by -\frac{1}{3} undoes the multiplication by -\frac{1}{3}.

$$x=\frac{5y+1}{-\frac{1}{3}}$$

Divide 5y+1 by -\frac{1}{3} by multiplying 5y+1 by the reciprocal of -\frac{1}{3}.

$$x=-15y-3$$

Solve for y

$$y=-\frac{x}{15}-\frac{1}{5}$$

Steps for Solving Linear Equation

Combine 6y and -y to get 5y.

$$\frac{2}{3}x-1=5y+x$$

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

$$5y+x=\frac{2}{3}x-1$$

Subtract x from both sides.

$$5y=\frac{2}{3}x-1-x$$

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

$$5y=-\frac{1}{3}x-1$$

The equation is in standard form.

$$5y=-\frac{x}{3}-1$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{-\frac{x}{3}-1}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{-\frac{x}{3}-1}{5}$$

Divide -\frac{x}{3}-1 by 5.

$$y=-\frac{x}{15}-\frac{1}{5}$$